%% GI.bib %% ============================================= %% Bibliography of Generalized Inverses %% Compiled by Adi Ben-Israel %% Updated: 24 May 01 %% ============================================= %% Comments, additions & changes would be appreciated. %% Please send to: %% Adi Ben-Israel %% RUTCOR - Rutgers University %% 640 Bartholomew Rd %% Piscataway, NJ 08854-8003 %% %% E-mail: %% Tel: +1-732-445-5631 %% Fax: +1-732-445-5472 %% ============================================ %% Abbreviations used in KEYWORDS field: %% %% alg : algebraic content %% algf : general fields (genf) %% algid : integral domain %% alglin: linear algebra %% algmul: multilinear algebra %% algr : rings %% algsg : semi groups %% ana : analytic content %% app : application %% appalgo: application in algorithms %% appana: application in analysis %% appcon: application to optimal control %% appdif: application to differential equations %% appdig: application to differential gemoetry %% appfrm: application to frames & wavelets %% appgeo: application to geometry and geodesy %% appint: application to integration %% appit : application to iterative methods %% appmar: application to Markov processes %% appnet: application to networks %% appopt: application to optimization %% appvis: application in vision and pattern recognition %% apphys: application to physics %% approb: application to probability %% appst : application to statistics %% aprx : approximation problems %% bibl : useful bibliography %% comb : combinatorics %% comp : computational content %% compdi: directional method (dirc) %% compex: exact computation %% compdec: decomposition methods %% compar: parallel computations %% compex: computational experience %% compGS: Gram-Schmidt methods %% compit: iterative methods (iter) %% compLU: LU methods (lud) %% comppr: programs (prog) %% compQR: QR decomposition (qrd) %% cond : condition numbers %% det : determinants %% detCr : Cramer rule %% detgen: generalized determinants %% diff : differential equations & operators %% discr : discrete problems %% his : history %% eig : eigenvalue problems %% eigen : generalized eigenvalue problems (geig) %% gen : general %% geo : geometric content (geom) %% geoa : principal or canonical angles (angl) %% geos : geometry of subspaces %% GauMar: Gauss Markov Theorem %% indx : index of matrix %% ineq : inequalities %% inteq : integral equations and operators %% inv : inverses in general %% inv1 : {1}-inverses %% inv2 : {2}-inverses %% inv12 : {1,2}-inverses %% invD : Drazin inverse %% invgr : group inverse %% invMP : Moore-Penrose inverse (mp) %% invnl : inverses of non-linear operators %% invo : other inverses %% jacob : Jacobians %% limrep: limit representations %% lineq : linear (vector) equations %% linop : linear operators (oper) %% lindif: linear differential operators %% linint: linear integral operators %% lp : linear programming %% lsq : least squares problems %% lsqnl : non-linear least squares %% lsqtot: total least squares %% mat : matrices %% matbor: bordered matrices %% matder: matrix derivatives %% matEP : EP matrices %% mateq : linear matrix equations %% matfun: matrix functions %% matM : M-matrices %% matmon: monotone or non-negative matrices %% matord: order on matrices %% matpart: partitioned matrices %% matprod: products of matrices %% matpsd: PSD matrices %% matsum: sums of matrices %% matstr: special structure matrices %% matest : test matrices %% matvol: matrix volume %% mulgr : multigrid methods %% sol : solutions in general %% sollsq: least squares solutions %% solmin: minimum norm solutions (mins %% nlp : nonlinear optimization %% nls : nonlinear systems %% norm : general norms %% norm1 : 1-norm %% norm2 : Euclidean norm %% normC : Chebyshev norm %% normdu: dual norms %% parsum: parallel sums %% proj : projections %% projob: oblique projections %% pert : perturbation theory & error analysis %% reg : regression (regr) %% regrid: ridge regression (ridg) %% repcl : closed form %% replim: representations as limit %% repint: representation as integral %% reverse: reverse-order results %% serexp: series expansions (serx) %% spac : general spaces %% spacbi: space with bilinear form %% spacB : Banach spaces (bans) %% spacH : Hilbert space (hils) %% singv : singular values %% svd : singular value decomposition %% svdgen: generalized singular value decomposition (gsvd) %% ============================================ %% Abbreviations of Journal names: @string{AMEMM = "Amer. Math. Monthly"} @string{ANNIS = "Ann. Inst. Statist. Math."} @string{APPMC = "Appl. Math. Comput."} @string{BULAM1 = "Bull. Amer. Math. Soc."} @string{COMMA1 = "Comm. ACM"} @string{COMPJ = "Comput. J."} @string{COMPU = "Computing"} @string{DOKAN2 = "Dokl. Akad. Nauk SSSR"} @string{IEETA5 = "IEEE Trans. Automatic Control"} @string{IEETS2 = "IEEE Trans. Systems Man Cybernet."} @string{INDJM1 = "Indian J. Math."} @string{ISRJM = "Israel J. Math."} @string{JAMES = "J. Amer. Statist. Assoc."} @string{JAPPT1 = "J. Approximation Theory"} @string{JASSC = "J. Assoc. Comput. Mach."} @string{JAUSMA = "J. Austral. Math. Soc. Ser. A"} @string{JFRAI = "J. Franklin Inst."} @string{JLONM1 = "J. London Math. Soc."} @string{JMATA = "J. Math. Anal. Appl."} @string{JOPTT2 = "J. Optim. Theory Appl."} @string{LINAA1 = "Linear Algebra and its Applications"} @string{LINMA = "Linear and Multilinear Algebra"} @string{MATHC2 = "Math. Comput."} @string{MATPC = "Math. Proc. Cambridge Philos. Soc."} @string{NUMEM = "Numer. Math."} @string{OPERR1 = "Operations Res."} @string{PACJM = "Pacific J. Math."} @string{PROAM = "Proc. Amer. Math. Soc."} @string{PROCPS = "Proceedings of the Cambridge Philosophical Society"} @string{PRONA = "Proc. Nat. Acad. Sci. U.S.A."} @string{REVRM = "Rev. Roumaine Math. Pures Appl."} @string{PRRSLA = "Proc. Roy. Soc. London Ser. A"} @string{QUAAM = "Quart. Appl. Math."} @string{SANKA = "Sankhy{\=a} Ser. A"} @string{SANKB = "Sankhy{\=a} Ser. B"} @string{SIAJA1 = "SIAM J. Algebraic Discrete Methods"} @string{SIAJA = "SIAM J. Appl. Math."} @string{SIAJC1 = "SIAM J. Comput."} @string{SIAJC3 = "SIAM J. Control Optim."} @string{SIAJC2 = "SIAM J. Control Optimization"} @string{SIAJD = "SIAM J. Discrete Math."} @string{SIAJM = "SIAM J. Math. Anal."} @string{SIAJM1 = "SIAM J. Matrix Anal. Appl."} @string{SIAJN = "SIAM J. Numer. Anal."} @string{SIAJO = "SIAM J. Optim."} @string{SIAJS1 = "SIAM J. Sci. Comput."} @string{SIAJS = "SIAM J. Sci. Statist. Comput."} @string{SIAMR = "SIAM Rev."} @string{SOVMD = "Soviet Math. Dokl."} @string{TRAAM = "Trans. Amer. Math. Soc."} @string{ZANGM1 = "Z. Angew. Math. Mech."} @string{ZANGM2 = "Z. Angew. Math. Phys."} @string{ZVYCM1 = "Zh. Vychisl. Mat. i Mat. Fiz."} %% ===================================================== @preamble{ "\def\polhk#1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} " } @Article{Abdel-Malek97, author = {{Abdel-Malek}, K. and Yeh, {Harn-Jou}}, title = {On the determination of starting points for parametric surface intersections}, journal = {Computer-aided Design}, volume = {29}, number = {1}, year = {1997}, pages = {21--35}, keywords = {surface intersection; parametric surfaces; starting points; Moore-Penrose}, } @article {Abdelmalek74, AUTHOR = {Abdelmalek, N. N.}, TITLE = {On the solutions of the linear least squares problems and pseudo--inverses}, JOURNAL = COMPU, VOLUME = {13}, YEAR = {1974}, NUMBER = {3-4}, PAGES = {215--228}, MRCLASS = {65F20}, MRNUMBER = {52 \#15988}, KEYWORDS = {lsq,sollsq,compGS}, } @article {Adukov98, AUTHOR = {Adukov, V. M.}, TITLE = {Generalized inversion of block {T}oeplitz matrices}, JOURNAL = LINAA1, VOLUME = {274}, YEAR = {1998}, PAGES = {85--124}, MRCLASS = {47B35 (15A09 15A57)}, MRNUMBER = {99e:47030}, } @article {Adukov99, AUTHOR = {Adukov, V. M.}, TITLE = {Generalized inversion of finite rank {H}ankel and {T}oeplitz operators with rational matrix symbols}, JOURNAL = LINAA1, VOLUME = {290}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {119--134}, MRCLASS = {47B35 (15A09 47A05)}, MRNUMBER = {2000b:47071}, } @article {Afriat56, AUTHOR = {Afriat, S. N.}, TITLE = {On the latent vectors and characteristic values of products of pairs of symmetric idempotents}, JOURNAL = {Quart. J. Math. Oxford Ser. (2)}, VOLUME = {7}, YEAR = {1956}, PAGES = {76--78}, MRCLASS = {15.0X}, MRNUMBER = {18, 371a}, KEYWORDS = {proj, eig, matprod}, } @ARTICLE{Afriat57, AUTHOR = {Afriat, S. N.}, TITLE = {Orthogonal and oblique projectors and the characteristics of pairs of vector spaces}, JOURNAL = {Proc. Cambridge Philos. Soc.}, VOLUME = {53}, YEAR = {1957}, PAGES = {800--816}, MRCLASS = {62.00 (15.00)}, MRNUMBER = {20 \#1389}, KEYWORDS = {proj, projob, geoa, geos, appst}, } @book {AhlbergEtAl67, AUTHOR = {Ahlberg, J. H. and Nilson, E. N. and Walsh, J. L.}, TITLE = {The {T}heory of {S}plines and their {A}pplications}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1967}, PAGES = {xi+284}, MRCLASS = {41.30 (65.00)}, MRNUMBER = {39 \#684}, } @article {Aitken34, AUTHOR = {Aitken, A. C.}, TITLE = {On least squares and linear combinations of observations}, JOURNAL = {Proceedings of the Royal Society of Edinburgh, Sec A}, VOLUME = {55}, YEAR = {1934}, PAGES = {42--47}, } @TECHREPORT{AkatsukaMatsuo65, author = {Akatsuka, Y. and Matsuo, T.}, title = {Optimal control of linear discrete systems using the generalized inverse of a matrix}, institution = {Institute of Automatic Control, Nagoya Univ.}, year = {1965}, type = {Techn Rept.}, number = {13}, address = {Nagoya, Japan}, keywords = {}, } @article {Akdeniz77, AUTHOR = {Akdeniz, F.}, TITLE = {A note concerning the {G}auss-{M}arkov theorem}, JOURNAL = {J. Fac. Sci. Karadeniz Tech. Univ.}, FJOURNAL = {Karadeni\.z Teknik \"Universitesi Temel. Bilimler Fak\"ultesi. Dergisi. (Karadeniz Technical University. Faculty of Sciences. Journal.) Series MA: Mathematics}, VOLUME = {1}, YEAR = {1977}, PAGES = {129--133}, MRCLASS = {62J05}, MRNUMBER = {81m:62118}, } @article {AkdenizSweilem86, AUTHOR = {Akdeniz, F. and Sweilem, M.}, TITLE = {An application of the generalized inverse to the two way classification for estimating variance components}, JOURNAL = {J. Karadeniz Univ. Fac. Arts Sci. Ser. Math.-Phys.}, FJOURNAL = {Journal Karadeniz University. Faculty of Arts and Sciences. Series of Mathematics-Physics}, VOLUME = {9}, YEAR = {1986}, PAGES = {1--10}, MRCLASS = {62J10 (62H30)}, MRNUMBER = {88m:62106}, NOTE = {(extension of \cite{Speed74})}, } @article {AlaloufStyan79, AUTHOR = {Alalouf, I. S. and Styan, G. P. H.}, TITLE = {Characterizations of estimability in the general linear model}, JOURNAL = {Ann. Statist.}, FJOURNAL = {The Annals of Statistics}, VOLUME = {7}, YEAR = {1979}, NUMBER = {1}, PAGES = {194--200}, MRCLASS = {62J05}, MRNUMBER = {80g:62044}, } @article {AlaloufStyan79a, AUTHOR = {Alalouf, I. S. and Styan, G. P. H.}, TITLE = {Estimability and testability in restricted linear models}, JOURNAL = {Math. Operationsforsch. Statist. Ser. Statist.}, FJOURNAL = {Mathematische Operationsforschung und Statistik Series Statistics}, VOLUME = {10}, YEAR = {1979}, NUMBER = {2}, PAGES = {189--201}, MRCLASS = {62J05}, MRNUMBER = {82g:62088}, } @ARTICLE{Albert69, author = {Albert, A.}, title = {Conditions for positive and nonnegative definiteness in terms of pseudo--inverses}, journal = SIAJA, year = {1969}, volume = {17}, pages = {434--440}, keywords = {}, } @BOOK{Albert72, author = {Albert, A.}, title = {Regression and the {M}oore--{P}enrose {P}seudoinverse}, publisher = {Academic Press}, year = {1972}, address = {New York}, keywords = {}, } @ARTICLE{Albert73, author = {Albert, A.}, title = {The {G}auss--{M}arkov theorem for regression models with possibly singular covariances}, journal = SIAJA, year = {1973}, volume = {24}, pages = {182-187}, keywords = {}, } @inproceedings{Albert76, AUTHOR = {Albert, A.}, TITLE = {Statistical applications of the pseudo inverse}, CROSSREF = {Nashed76}, PAGES = {525--548}, } @ARTICLE{AlbertSittler65, author = {Albert, A. and Sittler, R. W.}, title = {A method for computing least squares estimators that keep up with the data}, journal = {SIAM J. Control}, year = {1965}, volume = {3}, pages = {384--417}, keywords = {}, } @incollection {AleksicRakocevic94, AUTHOR = {Aleksi{\'c}, V. and Rako{\v{c}}evi{\'c}, V.}, TITLE = {Approximate properties of the {M}oore-{P}enrose inverse}, BOOKTITLE = {{VIII} {C}onference on {A}pplied {M}athematics ({T}ivat, 1993)}, PUBLISHER = {Univ. Montenegro}, ADDRESS = {Podgorica}, YEAR = {1994, pp. 1--14}, MRCLASS = {47A50 (15A09 46H99 47A05 65F20)}, MRNUMBER = {96b:47007}, } @preamble{ "\def\cprime{$'$} " } @article {Aliev79, AUTHOR = {Aliev, B. A.}, TITLE = {The pseudo-inverse operator for the product of two operators}, JOURNAL = {Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet.}, FJOURNAL = {Vestnik Moskovskogo Universiteta. Seriya XV. Vychislitel\cprime naya Matematika i Kibernetika}, YEAR = {1979}, NUMBER = {2}, PAGES = {11--15, 70}, ISSN = {0137-0782}, MRCLASS = {47A05 (65J10)}, MRNUMBER = {80h:47002}, } @article {AllamLaughton76, AUTHOR = {Allam, M. F. and Laughton, M. A.}, TITLE = {The use of pseudo and oblique pseudo-inverse matrices in power system state estimation algorithms}, JOURNAL = {Internat. J. Control}, VOLUME = {24}, YEAR = {1976}, NUMBER = {5}, PAGES = {661--671}, MRCLASS = {93E10}, MRNUMBER = {54 \#14848}, } @article {AllgowerEtAl99, AUTHOR = {Allgower, E. L. and B{\"o}hmer, K. and Hoy, A. and Janovsk{\'y}, V.}, TITLE = {Direct methods for solving singular nonlinear equations}, JOURNAL = {ZAMM Z. Angew. Math. Mech.}, VOLUME = {79}, YEAR = {1999}, NUMBER = {}, PAGES = {219--231}, MRCLASS = {}, MRNUMBER = {}, } @incollection {AllgowerGeorg97, AUTHOR = {Allgower, E. L. and Georg, K.}, TITLE = {Numerical path following}, BOOKTITLE = {Handbook of {N}umerical {A}nalysis, {V}ol. {V}}, PAGES = {3--207}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1997}, MRCLASS = {65Hxx}, MRNUMBER = {1 470 225}, KEYWORDS = {Newton, predictor-corrector, path-following}, } @article {AlpayEtAl00, AUTHOR = {Alpay, D. and Ball, J. A. and Bolotnikov, V.}, TITLE = {On the bitangential interpolation problem for contractive valued functions in the polydisk}, JOURNAL = {J. Operator Theory}, FJOURNAL = {Journal of Operator Theory}, VOLUME = {44}, YEAR = {2000}, NUMBER = {2}, PAGES = {277--301}, MRCLASS = {47A57}, MRNUMBER = {1 794 820}, KEYWORDS = {Interpolation, operator methods, local analytic geometry, reproducing kernels}, } @article {AlpayEtAl96, AUTHOR = {Alpay, D. and Bolotnikov, V. and Loubaton, Ph.}, TITLE = {One two-sided residue interpolation for matrix-valued {$H\sb 2$}-functions with symmetries}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {200}, YEAR = {1996}, NUMBER = {1}, PAGES = {76--105}, MRCLASS = {47A57 (30D55 30E05 41A30 46E99)}, MRNUMBER = {97e:47019}, KEYWORDS = {Interpolation, operator methods, ${H}^p$-classes, reproducing kernels}, } @article {AlpayEtAl01, AUTHOR = {Alpay, D. and Bolotnikov, V. and Rodman, L.}, TITLE = {Two-sided tangential interpolation for {H}ilbert-{S}chmidt operator functions on polydisks}, JOURNAL = {Operator Theory: Advances and Applications}, VOLUME = {124}, YEAR = {2001}, PAGES = {21--62}, MRCLASS = {47A56 41A05 (32A35)}, MRNUMBER = {}, KEYWORDS = {Interpolation, operator methods, operator valued functions, ${H}^p$-classes, reproducing kernels}, } @article {AlpayEtAl99, AUTHOR = {Alpay, D. and Bolotnikov, V. and Rodman, L.}, TITLE = {One-sided tangential interpolation for operator-valued {H}ardy functions on polydisks}, JOURNAL = {Integral Equations Operator Theory}, FJOURNAL = {Integral Equations and Operator Theory}, VOLUME = {35}, YEAR = {1999}, NUMBER = {3}, PAGES = {253--270}, ISSN = {0378-620X}, MRCLASS = {47A57 (32A35 32E30)}, MRNUMBER = {2000f:47023}, KEYWORDS = {Interpolation, operator methods, operator valued functions, ${H}^p$-classes, reproducing kernels}, } @ARTICLE{Altman55, author = {Altman, M.}, title = {A generalization of {N}ewton's method}, journal = {Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.}, year = {1955}, volume = {3}, pages = {189--193}, keywords = {}, } @ARTICLE{Altman57, author = {Altman, M.}, title = {On a generalization of {N}ewton's method}, journal = {Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.}, year = {1957}, volume = {5}, pages = {789--795}, keywords = {}, } @inproceedings{AmburgeyEtAl68, AUTHOR = {Amburgey, J. K. and Lewis, T. O. and Boullion, T. L.}, TITLE = {On computing generalized characteristic vectors and values for a rectangular matrix}, CROSSREF = {BoullionOdell68}, PAGES = {267--275}, YEAR = {1968}, KEYWORDS = {}, } @ARTICLE{AmirMoez70, author = {Amir-Mo{\'e}z, A. R.}, title = {Geometry of generalized inverses}, journal = {Math. Mag.}, year = {1970}, volume = {43}, pages = {33--36}, keywords = {}, } @article {AmirMoez73, AUTHOR = {Amir-Mo{\'e}z, A. R.}, TITLE = {Quasi-singular values of linear transformations}, JOURNAL = {Rend. Circ. Mat. Palermo (2)}, VOLUME = {22}, YEAR = {1973}, NUMBER = {3}, PAGES = {314--316 (1974)}, MRCLASS = {15A18}, MRNUMBER = {55 \#10480}, } @article {AmirMoez75, AUTHOR = {Amir-Mo{\'e}z, A. R.}, TITLE = {Geometry of determinants and {G}rassmann algebras}, JOURNAL = {Delta (Waukesha)}, VOLUME = {5}, YEAR = {1975}, NUMBER = {2}, PAGES = {71--83}, MRCLASS = {15A75}, MRNUMBER = {52 \#3205}, } @book {AmirMoez90, AUTHOR = {Amir-Mo{\'e}z, A. R.}, TITLE = {Extreme {P}roperties of {L}inear {T}ransformations}, PUBLISHER = {Polygonal Publ. House}, ADDRESS = {Washington, NJ}, YEAR = {1990}, PAGES = {viii+166}, ISBN = {0-936428-12-0}, MRCLASS = {15-02 (15A18)}, MRNUMBER = {93a:15001}, } @article {AmirMoezByerly96, AUTHOR = {Amir-Mo{\'e}z, A. R. and Byerly, R. E.}, TITLE = {Pythagorean theorem in unitary spaces}, JOURNAL = {Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.}, VOLUME = {7}, YEAR = {1996}, PAGES = {85--89}, MRCLASS = {51M25}, MRNUMBER = {97d:51033}, } @article {AmirMoezHorn58, AUTHOR = {Amir-Mo{\'e}z, A. R. and Horn, A.}, TITLE = {Singular values of a matrix}, JOURNAL = AMEMM, VOLUME = {65}, YEAR = {1958}, PAGES = {742--748}, MRCLASS = {15.00}, MRNUMBER = {20 \#7037}, } @MASTERSTHESIS{AndersonCL67, author = {Anderson, C. L.}, title = {A {G}eometric {T}heory of {P}seudoinverses and some {A}pplications in {S}tatistics}, school = {Southern Methodist Univ.}, year = {1967}, type = {Master's thesis in Statistics}, keywords = {}, } @article {AndersonRDEtAl84, AUTHOR = {Anderson, R. D. and Henderson, H. V. and Pukelsheim, F. and Searle, S. R.}, TITLE = {Best estimation of variance components from balanced data, with arbitrary kurtosis}, JOURNAL = {Math. Operationsforsch. Statist. Ser. Statist.}, FJOURNAL = {Mathematische Operationsforschung und Statistik Series Statistics}, VOLUME = {15}, YEAR = {1984}, NUMBER = {2}, PAGES = {163--176}, MRCLASS = {62J10}, MRNUMBER = {85k:62157}, } @ARTICLE{Anderson71, author = {Anderson, Jr., W. N.}, title = {Shorted operators}, journal = SIAJA, year = {1971}, volume = {20}, pages = {520--525}, keywords = {}, } @ARTICLE{AndersonDuffin69, author = {Anderson, Jr., W. N. and Duffin, R. J.}, title = {Series and parallel addition of matrices}, journal = SIAJA, year = {1969}, volume = {26}, pages = {576--594}, keywords = {}, NOTE = {(see \cite{Krafft98})}, } @article {AndersonSchreiber72, AUTHOR = {Anderson, Jr., W. N. and Schreiber, M.}, TITLE = {The infimum of two projections}, JOURNAL = {Acta Sci. Math. (Szeged)}, VOLUME = {33}, YEAR = {1972}, PAGES = {165--168}, MRCLASS = {46C05}, MRNUMBER = {48 \#848}, KEYWORDS = {Hilbert, projection on intersection}, } @article {AndersonTrapp75, AUTHOR = {Anderson, Jr., W. N. and Trapp, G. E.}, TITLE = {Shorted operators. {I}{I}}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {28}, YEAR = {1975}, PAGES = {60--71}, MRCLASS = {94A20 (47-XX)}, MRNUMBER = {50 \#9417}, NOTE = {(this concept first introduced by Krein \cite{Krein47})}, } @article {AndersonTrapp75a, AUTHOR = {Anderson, Jr., W. N. and Trapp, G. E.}, TITLE = {Inequalities for the parallel connection of resistive $n$-port networks}, JOURNAL = {J. Franklin Inst.}, VOLUME = {209}, YEAR = {1975}, NUMBER = {5}, PAGES = {305--313}, MRCLASS = {94A20}, MRNUMBER = {55 \#2365}, } @inproceedings{AndersonTrapp82, AUTHOR = {Anderson, Jr., W. N. and Trapp, G. E.}, TITLE = {Analytic operator functions and electrical networks}, CROSSREF = {Campbell82a}, PAGES = {12--26}, YEAR = {1982}, MRCLASS = {47A56 (94C05)}, KEYWORDS = {appnet}, MRNUMBER = {84i:47022}, } @article {AndersonTrapp86, AUTHOR = {Anderson, Jr., W. N. and Trapp, G. E.}, TITLE = {Inverse problems for means of matrices}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, VOLUME = {7}, YEAR = {1986}, NUMBER = {2}, PAGES = {188--192}, MRCLASS = {15A24 (47A62)}, MRNUMBER = {87c:15028}, KEYWORDS = {parallel sum, mean}, } @article {Ando79, AUTHOR = {Ando, T.}, TITLE = {Generalized {S}chur complements}, JOURNAL = LINAA1, VOLUME = {27}, YEAR = {1979}, PAGES = {173--186}, MRCLASS = {15A24}, MRNUMBER = {80m:15005}, KEYWORDS = {Schur complement}, } @article {AnitescuEtAl96, AUTHOR = {Anitescu, Mihai and Coroian, Dan I. and Nashed, M. Zuhair and Potra, Florian A.}, TITLE = {Outer inverses and multi-body system simulation}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = {Numerical Functional Analysis and Optimization. An International Journal}, VOLUME = {17}, YEAR = {1996}, NUMBER = {7-8}, PAGES = {661--678}, MRCLASS = {65L05 (34A09 70-08 70E99 70F20)}, MRNUMBER = {98b:65073}, } @article {AnseloneLaurent68, AUTHOR = {Anselone, P. M. and Laurent, P. J.}, TITLE = {A general method for the construction of interpolating or smoothing spline-functions}, JOURNAL = {Numer. Math.}, VOLUME = {12}, YEAR = {1968}, PAGES = {66--82}, MRCLASS = {41.60 (65.00)}, MRNUMBER = {40 \#3145}, } @article {AntonDuris76, AUTHOR = {Anton, H. and Duris, C. S.}, TITLE = {On minimum norm and best approximate solutions of ${A}v=b$ in normed spaces}, JOURNAL = {J. Approximation Theory}, VOLUME = {16}, YEAR = {1976}, NUMBER = {3}, PAGES = {245--250}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {54 \#1587}, } @article {Antoulas98, AUTHOR = {Antoulas, A. C.}, TITLE = {Approximation of linear operators in the $2$-norm}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {278}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {309--316}, MRCLASS = {15A60 (47A58 47B35)}, MRNUMBER = {99g:15033}, } @BOOK{Archibald38, author = {Archibald, R. C.}, title = {A {S}emicentennial {H}istory of the {A}merican {M}athematical {S}ociety 1888--1938 (2 volumes)}, publisher = {American Mathematical Society}, year = {1938}, volume = {}, address = {New York}, KEYWORDS = {History, Moore}, } @ARTICLE{Arghiriade63, author = {Arghiriade, E.}, title = {Sur les matrices qui sont permutables avec leur inverse g\'en\'eralis\'ee}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1963}, volume = {35}, pages = {244--251}, keywords = {}, } @ARTICLE{Arghiriade67, author = {Arghiriade, E.}, title = {Remarques sur l'inverse g\'en\'eralis\'ee d'un produit de matrices}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1967}, volume = {42}, pages = {621--625}, keywords = {}, } @article {Arghiriade67a, AUTHOR = {Arghiriade, E.}, TITLE = {On the generalized inverse of a product of matrices}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {5}, YEAR = {1967}, PAGES = {37--42}, MRCLASS = {15.15}, MRNUMBER = {38 \#1105}, } @article {Arghiriade67b, AUTHOR = {Arghiriade, E.}, TITLE = {Sur quelques \'equations fonctionnelles de matrices}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, VOLUME = {12}, YEAR = {1967}, PAGES = {1127--1133}, MRCLASS = {39.37}, MRNUMBER = {38 \#1425}, } @ARTICLE{Arghiriade68, author = {Arghiriade, E.}, title = {Sur l'inverse g\'en\'eralis\'ee d'un operateur lineaire dans les espaces de {H}ilbert}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1968}, volume = {45}, pages = {471--477}, keywords = {}, } @article {ArghiriadeDragomir63, AUTHOR = {Arghiriade, E. and Dragomir, A.}, TITLE = {Une nouvelle d\'efinition de l'inverse g\'en\'eralis\'ee d'une matrice}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {35}, YEAR = {1963}, PAGES = {158--165}, MRCLASS = {15.15}, MRNUMBER = {31 \#3439}, } @ARTICLE{ArghiriadeDragomir69, author = {Arghiriade, E. and Dragomir, A.}, title = {Remarques sur quelques th\'eoremes relatives a l'inverse g\'en\'eralis\'ee d'un operateur lineaire dans les espaces de Hilbert}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1969}, volume = {46}, pages = {333--338}, keywords = {}, } @article {Argyros00, AUTHOR = {Argyros, I. K.}, TITLE = {Local convergence theorems of {N}ewton's method for nonlinear equations using outer or generalized inverses}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {50(125)}, YEAR = {2000}, NUMBER = {3}, PAGES = {603--614}, MRCLASS = {65J15 (47J25)}, MRNUMBER = {1 777 480}, } @article {AronowitzEichinger75, AUTHOR = {Aronowitz, S. and Eichinger, B. E.}, TITLE = {Petrie matrices and generalized inverses}, JOURNAL = {J. Math. Phys.}, VOLUME = {16}, YEAR = {1975}, PAGES = {1278--1283}, MRCLASS = {15A09}, MRNUMBER = {54 \#2677}, } @article {Aronszajn50, AUTHOR = {Aronszajn, N.}, TITLE = {Theory of reproducing kernels}, JOURNAL = TRAAM, VOLUME = {68}, YEAR = {1950}, PAGES = {337--404}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {reproducing kernels}, } @article {AtkinsonFV51, AUTHOR = {Atkinson, F. V.}, TITLE = {The normal solvability of linear equations in normed spaces (Russian)}, JOURNAL = {Mat. Sbornik N.S.}, VOLUME = {28(70)}, YEAR = {1951}, PAGES = {3--14}, MRCLASS = {}, KEYWORDS = {}, MRNUMBER = {13 \#46d}, } @article {AtkinsonFV53, AUTHOR = {Atkinson, F. V.}, TITLE = {On relatively regular operators}, JOURNAL = {Acta Sci. Math. Szeged}, VOLUME = {15}, YEAR = {1953}, PAGES = {38--56}, MRCLASS = {}, KEYWORDS = {}, MRNUMBER = {15 \#134e}, } @article {AtkinsonKE67, AUTHOR = {Atkinson, K. E.}, TITLE = {The solution of non-unique linear integral equations}, JOURNAL = NUMEM, VOLUME = {10}, YEAR = {1967}, PAGES = {117--124}, MRCLASS = {45.10 (65.00)}, KEYWORDS = {inteq, linint, solmin}, MRNUMBER = {36 \#3082}, NOTE = {(see also \cite{MooreNashed74})}, } @ARTICLE{Autonne02, author = {Autonne, L.}, title = {Sur les groupes lin{\'e}aires, r{\'e}els et orthogonaux}, journal = {Bull. Soc. Math. France}, year = {1902}, volume = {30}, pages = {121--134}, keywords = {}, } @ARTICLE{Autonne15, author = {Autonne, L.}, title = {Sur les matrices hypohermitiennes et sur les matrices unitaires}, journal = {Ann. Univ. Lyon, Nouvelle S{\'e}r. I}, year = {1915}, volume = {38}, pages = {1--77}, keywords = {}, NOTE = {(see history of SVD in \cite{Stewart93})}, } @article {AvrachenkovEtAl01, AUTHOR = {Avrachenkov, K. E. and Haviv, M. and Howlett, P. G.}, TITLE = {Inversion of analytic matrix functions that are singular at the origin}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {22}, YEAR = {2001}, NUMBER = {4}, PAGES = {1175--1189 (electronic)}, MRCLASS = {15A09 (47A56)}, MRNUMBER = {1 824 064}, KEYWORDS = {Matrix valued functions, Laurent series}, } @article {Azumaya54, AUTHOR = {Azumaya, Gor\^{o}}, TITLE = {Strongly $\pi$-regular rings}, JOURNAL = {J. Fac. Sci. Hokkaido Univ. Ser. I.}, VOLUME = {13}, YEAR = {1954}, PAGES = {34--39}, MRCLASS = {09.1X}, MRNUMBER = {16,788e}, } @article {Backus70, AUTHOR = {Backus, G.}, TITLE = {Inference from inadequate and inaccurate data. {I}, {I}{I}}, JOURNAL = {Proc. Nat. Acad. Sci. U.S.A. 65 (1970), 1--7; ibid.}, VOLUME = {65}, YEAR = {1970}, PAGES = {281--287}, MRCLASS = {62.05}, MRNUMBER = {40 \#8150}, } @article {BackusGilbert70, AUTHOR = {Backus, G. and Gilbert, F.}, TITLE = {Uniqueness in the inversion of inaccurate gross {E}arth data}, JOURNAL = {Philos. Trans. Roy. Soc. London Ser. A}, VOLUME = {266}, YEAR = {1970}, NUMBER = {1173}, PAGES = {123--192}, MRCLASS = {86.65}, MRNUMBER = {56 \#7763}, } @article {BadeaMbekhta97, AUTHOR = {Badea, C. and Mbekhta, M.}, TITLE = {Generalized inverses and the maximal radius of regularity of a {F}redholm operator}, JOURNAL = {Integral Equations Operator Theory}, VOLUME = {28}, YEAR = {1997}, NUMBER = {2}, PAGES = {133--146}, MRCLASS = {47A53 (47A05)}, MRNUMBER = {98e:47018}, } @article {BadeaMbekhta99, AUTHOR = {Badea, C. and Mbekhta, M.}, TITLE = {Compressions of resolvents and maximal radius of regularity}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {351}, YEAR = {1999}, NUMBER = {7}, PAGES = {2949--2960}, MRCLASS = {47A10 (47A20 47A58)}, MRNUMBER = {99j:47005}, } @article {Baksalary86, AUTHOR = {Baksalary, J. K.}, TITLE = {A relationship between the star and minus orderings}, JOURNAL = LINAA1, VOLUME = {82}, YEAR = {1986}, PAGES = {163--167}, } @article {Baksalary02, AUTHOR = {Baksalary, J. K. and Baksalary, O. M.}, TITLE = {Commutativity of projectors}, JOURNAL = LINAA1, VOLUME = {341}, YEAR = {2002}, PAGES = {129--142}, } @article {BaksalaryHauke87, AUTHOR = {Baksalary, J. K. and Hauke, J.}, TITLE = {Partial orderings of matrices referring to singular values or eigenvalues}, JOURNAL = LINAA1, VOLUME = {96}, YEAR = {1987}, PAGES = {17--26}, MRCLASS = {}, MRNUMBER = {}, } @article {BaksalaryKala79, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {The matrix equation ${A}{X}-{Y}{B}={C}$}, JOURNAL = LINAA1, VOLUME = {25}, YEAR = {1979}, PAGES = {41--43}, MRCLASS = {15A24 (15A09)}, MRNUMBER = {80d:15014}, } @article {BaksalaryKala80, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {The matrix equation ${A}{X}{B}+{C}{Y}{D}={E}$}, JOURNAL = LINAA1, VOLUME = {30}, YEAR = {1980}, PAGES = {141--147}, MRCLASS = {15A24 (15A09)}, MRNUMBER = {82e:15010}, } @article {BaksalaryKala80a, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {Two properties of a nonnegative definite matrix}, JOURNAL = {Bull. Acad. Polon. Sci. S\'er. Sci. Math.}, FJOURNAL = {L'Acad\'emie Polonaise des Sciences. Bulletin. S\'erie des Sciences Math\'ematiques}, VOLUME = {28}, YEAR = {1980}, NUMBER = {5-6}, PAGES = {233--235 (1981)}, MRCLASS = {15A48}, MRNUMBER = {82i:15020}, } @article {BaksalaryKala83, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {Range invariance of certain matrix products}, JOURNAL = LINMA, VOLUME = {14}, YEAR = {1983}, NUMBER = {1}, PAGES = {89--96}, MRCLASS = {15A60}, MRNUMBER = {86a:15030}, } @article {BaksalaryKala84, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {Corrigendum: ``{O}n equalities between {B}{L}{U}{E}s, {W}{L}{S}{E}s, and {S}{L}{S}{E}s''}, JOURNAL = {Canad. J. Statist.}, FJOURNAL = {The Canadian Journal of Statistics. La Revue Canadienne de Statistique}, VOLUME = {12}, YEAR = {1984}, NUMBER = {3}, PAGES = {240}, ISSN = {0319-5724}, MRCLASS = {62J05}, MRNUMBER = {86f:62100b}, } @article {BaksalaryKala83a, AUTHOR = {Baksalary, J. K. and Kala, R.}, TITLE = {On equalities between {B}{L}{U}{E}s, {W}{L}{S}{E}s, and {S}{L}{S}{E}s}, JOURNAL = {Canad. J. Statist.}, FJOURNAL = {The Canadian Journal of Statistics. La Revue Canadienne de Statistique}, VOLUME = {11}, YEAR = {1983}, NUMBER = {2}, PAGES = {119--123}, ISSN = {0319-5724}, MRCLASS = {62J05}, MRNUMBER = {86f:62100a}, NOTE = {(extension of \cite{Lowerre74})}, } @article {BaksalaryMathew90, AUTHOR = {Baksalary, J. K. and Mathew, T.}, TITLE = {Rank invariance criterion and its application to the unified theory of least squares}, JOURNAL = LINAA1, VOLUME = {127}, YEAR = {1990}, PAGES = {393--401}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {91g:15002}, } @article {BaksalaryMitra91, AUTHOR = {Baksalary, J. K. and Mitra, S. K.}, TITLE = {Left-star and right-star partial orderings}, JOURNAL = LINAA1, VOLUME = {149}, YEAR = {1991}, PAGES = {73--89}, MRCLASS = {}, MRNUMBER = {}, } @article {BaksalaryPordzik90, AUTHOR = {Baksalary, J. K. and Pordzik, P. R. and Trenkler, G.}, TITLE = {A note on generalized ridge estimators}, JOURNAL = {Comm. Statist. Theory Methods}, VOLUME = {19}, YEAR = {1990}, NUMBER = {8}, PAGES = {2871--2877}, MRCLASS = {62J07}, MRNUMBER = {91k:62068}, } @article{BaksalaryPukelsheim91, AUTHOR = {Baksalary, J. K. and Pukelsheim, F.}, TITLE = {On the {L}{\"o}wner, minus, and star partial orderings of nonnegative definite matrices and their squares}, JOURNAL = LINAA1, VOLUME = {151}, YEAR = {1991}, PAGES = {135--141}, MRCLASS = {15A99}, MRNUMBER = {92e:15036}, } @article{BaksalaryEtAl92, AUTHOR = {Baksalary, J. K. and Puntanen, S. and Yanai, H.}, TITLE = {Canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix}, JOURNAL = LINAA1, VOLUME = {176}, YEAR = {1992}, PAGES = {61--74}, MRCLASS = {62H20}, MRNUMBER = {94d:62147}, } @article{BaksalaryEtAl89, AUTHOR = {Baksalary, J. K. and Pukelsheim, F. and Styan, G. P. H.}, TITLE = {Some properties of matrix partial orderings}, JOURNAL = LINAA1, VOLUME = {119}, YEAR = {1989}, PAGES = {57--85}, MRCLASS = {}, MRNUMBER = {}, } @article{BaksalaryEtAl96, AUTHOR = {Baksalary, J. K. and {\v{S}}emrl, P. and Styan, G. P. H.}, TITLE = {A note on rank--aditivity and range--aditivity}, JOURNAL = LINAA1, VOLUME = {237--238}, YEAR = {1996}, PAGES = {489--498}, MRCLASS = {}, MRNUMBER = {}, } @ARTICLE{Balakrishnan63, author = {Balakrishnan, A. V.}, title = {An operator theoretic formulation of a class of control problems and a steepest descent method of solution}, journal = {J. Soc. Indust. Appl. Math. Ser. A: Control}, year = {1963}, volume = {1}, pages = {109--127}, keywords = {}, } @article {BaldwinHoerl78, AUTHOR = {Baldwin, K. F. and Hoerl, A. E.}, TITLE = {Bounds of minimum mean squared error in ridge regression}, JOURNAL = {Comm. Statist. A---Theory Methods}, FJOURNAL = {Communications in Statistics. A. Theory and Methods}, VOLUME = {7}, YEAR = {1978}, NUMBER = {13}, PAGES = {1209--1218}, MRCLASS = {62J07}, MRNUMBER = {80h:62051}, } @article {BallEtAl94, AUTHOR = {Ball, J. A. and Rakowski, M. and Wyman, B. F.}, TITLE = {Coupling operators, {W}edderburn-{F}orney spaces, and generalized inverses}, JOURNAL = LINAA1, VOLUME = {203/204}, YEAR = {1994}, PAGES = {111--138}, MRCLASS = {15A09 (65J15)}, MRNUMBER = {95c:15005}, } @ARTICLE{Banerjee66, author = {Banerjee, K. S.}, title = {Singularity in {H}otelling's weighing designs and generalized inverses}, journal = {Ann. Math. Statist.}, year = {1966}, volume = {37}, pages = {1021--1032}, keywords = {}, NOTE = {(erratum, \textit{ibid} \textbf{40}(1969), 710)}, } @ARTICLE{BanerjeeFederer68, author = {Banerjee, K. S. and Federer, W. T.}, title = {On the structure and analysis of singular fractional replicates}, journal = {Ann. Math. Statist.}, year = {1968}, volume = {39}, pages = {657--663}, keywords = {}, } @article {Bapat94, AUTHOR = {Bapat, R. B.}, TITLE = {Generalized inverses with proportional minors}, JOURNAL = LINAA1, VOLUME = {211}, YEAR = {1994}, PAGES = {27--33}, MRCLASS = {15A09}, MRNUMBER = {95h:15005}, } @article {Bapat97, AUTHOR = {Bapat, R. B.}, TITLE = {Moore--{P}enrose inverse of the incidence matrix of a tree}, JOURNAL = LINMA, VOLUME = {42}, YEAR = {1997}, NUMBER = {2}, PAGES = {159--167}, MRCLASS = {15A09 (05C05 05C50)}, MRNUMBER = {98c:15012}, } @article {Bapat98, AUTHOR = {Bapat, R. B.}, TITLE = {Structure of a nonnegative regular matrix and its generalized inverses}, JOURNAL = LINAA1, VOLUME = {268}, YEAR = {1998}, PAGES = {31--39}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {98m:15009}, KEYWORDS = {matmon}, } @article {Bapat99, AUTHOR = {Bapat, R. B.}, TITLE = {Linear estimation in models based on a graph}, JOURNAL = LINAA1, VOLUME = {302/303}, YEAR = {1999}, PAGES = {223--230}, MRCLASS = {15A09 (05C05 05C50)}, MRNUMBER = {2000h:15006}, } @article {Bapat99a, AUTHOR = {Bapat, R. B.}, TITLE = {Resistance distance in graphs}, JOURNAL = {Mathematics Student}, VOLUME = {68}, YEAR = {1999}, PAGES = {87--98}, } @book {Bapat99b, AUTHOR = {Bapat, R. B.}, TITLE = {Linear {A}lgebra and {L}inear {M}odels}, EDITION = {Second}, PUBLISHER = {Hindustan Book Agency}, ADDRESS = {New Delhi}, YEAR = {1999}, PAGES = {xii+180}, ISBN = {81-85931-21-6}, MRCLASS = {}, MRNUMBER = {}, } @article {Bapat00, AUTHOR = {Bapat, R. B.}, TITLE = {Moore-{P}enrose inverse of set inclusion matrices}, JOURNAL = LINAA1, VOLUME = {318}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {35--44}, MRCLASS = {15A09}, MRNUMBER = {1 787 222}, } @article {Bapat02, AUTHOR = {Bapat, R. B.}, TITLE = {Outer inverses: {J}acobi type identities and nullities of submatrices}, JOURNAL = {To appear}, VOLUME = {}, YEAR = {2002}, NUMBER = {}, PAGES = {}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Jacobi identities, 2-inverses}, } @article {BapatBen-Israel95, AUTHOR = {Bapat, R. B. and Ben-Israel, A.}, TITLE = {Singular values and maximum rank minors of generalized inverses}, JOURNAL = LINMA, VOLUME = {40}, YEAR = {1995}, NUMBER = {2}, PAGES = {153--161}, MRCLASS = {15A18 (15A09)}, MRNUMBER = {98a:15019}, KEYWORDS = {singv, matvol, ineq, inv1, invMP}, } @inproceedings{BapatHartwig94, AUTHOR = {Bapat, R. B. and Hartwig, R. E.}, TITLE = {A master of the row space and the column space: the mathematical work of {S}ujit {K}umar {M}itra}, CROSSREF = {BapatEtAl94}, YEAR = {1994}, PAGES = {5--14}, MRCLASS = {01A60 (15-03)}, MRNUMBER = {1 295 867}, KEYWORDS = {his, bibl}, } @article {BapatEtAl97, AUTHOR = {Bapat, R. B. and Jain, S. K. and Pati, S.}, TITLE = {Weighted {M}oore-{P}enrose inverse of a {B}oolean matrix}, JOURNAL = LINAA1, VOLUME = {255}, YEAR = {1997}, PAGES = {267--279}, MRCLASS = {15A09}, MRNUMBER = {98a:15007}, KEYWORDS = {discr, invMP, invo}, } @article {BapatEtAl99, AUTHOR = {Bapat, R. B. and Jain, S. K. and Prasad, K. M.}, TITLE = {Generalized power symmetric stochastic matrices}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {127}, YEAR = {1999}, NUMBER = {7}, PAGES = {1987--1994}, MRCLASS = {15A51}, MRNUMBER = {99j:15032}, } @article {BapatEtAl97a, AUTHOR = {Bapat, R. B. and Jain, S. K. and Snyder, L. E.}, TITLE = {Nonnegative idempotent matrices and the minus partial order}, JOURNAL = LINAA1, VOLUME = {261}, YEAR = {1997}, PAGES = {143--154}, MRCLASS = {15A48}, MRNUMBER = {98c:15061}, KEYWORDS = {minus partial order}, } @incollection {BapatKulkarni00, AUTHOR = {Bapat, R. B. and Kulkarni, D. M.}, TITLE = {Minors of some matrices associated with a tree}, BOOKTITLE = {Algebra and Its {A}pplications. {C}ontemporary {M}athematics 259 (D. V. Huynh, S. K. Jain, S. R. Lopez-Permouth Ed.)}, PAGES = {45--66}, PUBLISHER = {American Math Society}, ADDRESS = {Providence, RI}, YEAR = {2000}, } @proceedings{BapatEtAl94, TITLE = {Generalized Inverses. Papers from the Workshop on $g$-inverses held in Calcutta, December 11--16, 1993}, EDITOR = {Bapat, R. B. and Mitra, S. K. and Hartwig, R.}, PUBLISHER = {North-Holland Publishing Co.}, ADDRESS = {New York}, YEAR = {1994}, PAGES = {i--v and 1--113}, MRCLASS = {15-06}, MRNUMBER = {1 295 866}, NOTE = {(special issue of \textit{Linear Algebra and its Applications} {\bf 211} (1994))}, KEYWORDS = {gen, his, bibl}, } @article {BapatPati98, AUTHOR = {Bapat, R. B. and Pati, Sukanta}, TITLE = {Algebraic connectivity and the characteristic set of a graph}, JOURNAL = LINMA, VOLUME = {45}, YEAR = {1998}, NUMBER = {2-3}, PAGES = {247--273}, MRCLASS = {05C50 (15A18)}, MRNUMBER = {99h:05082}, } @incollection {BapatPrasad99, AUTHOR = {Bapat, R. B. and Prasad, K. M.}, TITLE = {Cochran's Theorem and related results on matrix rank over a commutative ring}, BOOKTITLE = {Statistical {I}nference and {D}esign of {E}xperiments ({U}. {J}. {D}ixit and {M}. {R}. {S}atam Ed.)}, PAGES = {125--133}, PUBLISHER = {Narosa Publishing House}, ADDRESS = {}, YEAR = {1999}, } @book {BapatRaghavan97, AUTHOR = {Bapat, R. B. and Raghavan, T. E. S.}, TITLE = {Nonnegative {M}atrices and {A}pplications}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1997}, PAGES = {xiv+336}, ISBN = {0-521-57167-7}, MRCLASS = {15A48 (90A14 90C08)}, MRNUMBER = {98h:15038}, } @article {BapatEtAl90, AUTHOR = {Bapat, R. B. and Rao, K. P. S. Bhaskara and Prasad, K. M.}, TITLE = {Generalized inverses over integral domains}, JOURNAL = LINAA1, VOLUME = {140}, YEAR = {1990}, PAGES = {181--196}, MRCLASS = {15A09}, KEYWORDS = {algid, discr}, MRNUMBER = {91i:15006}, } @article {BapatRobinson92, AUTHOR = {Bapat, R. B. and Robinson, D. W.}, TITLE = {The {M}oore-{P}enrose inverse over a commutative ring}, JOURNAL = LINAA1, VOLUME = {177}, YEAR = {1992}, PAGES = {89--103}, MRCLASS = {15A09}, KEYWORDS = {invMP, algr}, MRNUMBER = {94a:15002}, } @article {BarkerCampbell83, AUTHOR = {Barker, G. P. and Campbell, S. L.}, TITLE = {Internal stability of two-dimensional systems}, JOURNAL = LINMA, VOLUME = {14}, YEAR = {1983}, NUMBER = {4}, PAGES = {365--369}, MRCLASS = {15A18}, MRNUMBER = {86g:15006}, } @article {Barnard63, AUTHOR = {Barnard, G. A.}, TITLE = {The logic of least squares}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {25}, YEAR = {1963}, PAGES = {124--127}, MRCLASS = {}, MRNUMBER = {30 \#2583}, } @BOOK{Barnett71, author = {Barnett, S.}, title = {Matrices in {C}ontrol {T}heory}, publisher = {Van Nostrand Reinhold}, year = {1971}, address = {London}, keywords = {}, } @BOOK{Barnett90, author = {Barnett, S.}, title = {Matrices: {M}ethods and {A}pplications}, publisher = {Clarendon Press}, year = {1990}, address = {Oxford}, keywords = {}, } @article {BartEtAl75, AUTHOR = {Bart, H. and Kaashoek, M. A. and Lay, D. C.}, TITLE = {Relative inverses of meromorphic operator functions and associated holomorphic projection functions}, JOURNAL = {Math. Ann.}, VOLUME = {218}, YEAR = {1975}, NUMBER = {3}, PAGES = {199--210}, MRCLASS = {47A55}, MRNUMBER = {53 \#3743}, } @article {Basile68, AUTHOR = {Basile, G.}, TITLE = {Alcune osservazioni sulla pseudoinversa di una matrice rettangolare. }, JOURNAL = {Atti Accad. Sci. Ist. Bologna Cl. Sci. Fis. Rend. (12)}, VOLUME = {6}, YEAR = {1968/1969}, NUMBER = {fasc.}, PAGES = {1--2, 236--240}, MRCLASS = {15.15}, MRNUMBER = {40 \#7276}, } @article {BaskettKatz69, AUTHOR = {Baskett, T. S. and Katz, I. J.}, TITLE = {Theorems on products of ${E}{P}\sb{r}$ matrices}, JOURNAL = LINAA1, VOLUME = {2}, YEAR = {1969}, PAGES = {87--103}, MRCLASS = {15.30}, MRNUMBER = {40 \#4280}, } @article{Bateman1908, author = {H. Bateman}, year = {1908}, title = {A Formula for the Solving Function of a Certain Integral Equation of the Second Kind}, journal = {Transactions of the Cambridge Philosophical Society}, volume = {20}, pages = {179-187}, KEYWORDS = {comp, svd, inteq}, } @article{Bateman1908a, author = {H. Bateman}, year = {1908}, title = {The Reality of the Roots of Certain Transcendental Equations Occurring in the Theory of Integral Equations}, journal = {Transactions of the Cambridge Philosophical Society}, volume = {20}, pages = {371--381}, KEYWORDS = {comp, svd, inteq}, } @article{Bateman1908b, author = {H. Bateman}, year = {1908}, title = {On the Application of Integral Equations to the Determination of Upper and Lower Limits of a Double Integral}, journal = {Transactions of the Cambridge Philosophical Society}, volume = {21}, pages = {123--128}, KEYWORDS = {comp, svd, inteq}, } @article{Bateman22, author = {H. Bateman}, year = {1922}, title = {On the Numerical Solution of Linear Integral Equations}, journal = PRRSLA, volume = {100}, pages = {441--449}, KEYWORDS = {comp, svd, inteq}, } @article {Batigne78, AUTHOR = {Batigne, D.}, TITLE = {Integral generalized inverses of integral matrices}, JOURNAL = LINAA1, VOLUME = {22}, YEAR = {1978}, PAGES = {125--134}, MRCLASS = {15A09}, KEYWORDS = {algr, discr}, MRNUMBER = {80c:15001}, } @article {BatigneEtAl78, AUTHOR = {Batigne, D. R. and Hall, F. J. and Katz, I. J.}, TITLE = {Further results on integral generalized inverses of integral matrices}, JOURNAL = LINMA, VOLUME = {6}, YEAR = {1978/79}, NUMBER = {3}, PAGES = {233--241}, MRCLASS = {15A36 (15A09)}, MRNUMBER = {80d:15020}, } @article {Bauer61, AUTHOR = {Bauer, F. L.}, TITLE = {A further generalization of the {K}antorovi\v c inequality}, JOURNAL = {Numer. Math.}, VOLUME = {3}, YEAR = {1961}, PAGES = {117--119}, MRCLASS = {15.58}, MRNUMBER = {23 \#A157}, } @ARTICLE{Bauer65, author = {Bauer, F. L.}, title = {Elimination with weighted row combinations for solving linear equations and least squares problems}, journal = NUMEM, year = {1965}, volume = {7}, pages = {338--352}, NOTE = {(republished, pp. 119--133 in \cite{WilkinsonReinsch71})}, } @TECHREPORT{Bauer67, author = {Bauer, F. L.}, title = {Theory of norms}, institution = {Stanford University}, year = {1967}, type = {Computer Science Dept.}, number = {CS 75}, address = {Stanford}, } @article {BauerEtAl61, AUTHOR = {Bauer, F. L. and Stoer, J. and Witzgall, C.}, TITLE = {Absolute and monotonic norms}, JOURNAL = {Numer. Math.}, VOLUME = {3}, YEAR = {1961}, PAGES = {257--264}, MRCLASS = {65.33 (15.58)}, MRNUMBER = {23 \#B3136}, } @BOOK{BeckenbachBellman71, author = {Beckenbach, E. F. and Bellman, R.}, title = {Inequalities}, publisher = {Springer-Verlag}, year = {1971}, address = {New York}, edition = {3rd}, } @BOOK{Bellman70, author = {Bellman, R.}, title = {Introduction to {M}atrix {A}nalysis}, publisher = {McGraw-Hill Book Co.}, year = {1970}, address = {New York}, edition = {2nd}, } @article{Beltrami1873, author = {E. Beltrami}, year = {1873}, title = {Sulle Funzioni Bilineari}, journal = {Giornale di Matematiche ad Uso degli Studenti Delle Universita}, volume = {11}, pages = {98-106}, NOTE = {(an English translation by D. Boley is available as University of Minnesota, Department of Computer Science, Technical Report 90--37, 1990. see history of SVD in \cite{Stewart93})}, KEYWORDS = {alglin, svd, his}, } @ARTICLE{Beltrami69, author = {Beltrami, E. J.}, title = {A constructive proof of the {K}uhn--{T}ucker multiplier rule}, journal = JMATA, year = {1969}, volume = {26}, pages = {297--306}, } @article {Ben-Israel64, AUTHOR = {Ben-Israel, A.}, TITLE = {On direct sum decompositions of {H}estenes algebras}, JOURNAL = ISRJM, VOLUME = {2}, YEAR = {1964}, PAGES = {50--54}, MRCLASS = {46.50}, KEYWORDS = {alg, mateq}, MRNUMBER = {30 \#1403}, } @article {Ben-Israel65, AUTHOR = {Ben-Israel, A.}, TITLE = {An iterative method for computing the generalized inverse of an arbitrary matrix}, JOURNAL = MATHC2, VOLUME = {19}, YEAR = {1965}, PAGES = {452--455}, MRCLASS = {65.35}, KEYWORDS = {compit, invMP}, MRNUMBER = {31 \#4152}, } @article {Ben-Israel65a, AUTHOR = {Ben-Israel, A.}, TITLE = {A modified {N}ewton-{R}aphson method for the solution of systems of equations}, JOURNAL = ISRJM, VOLUME = {3}, YEAR = {1965}, PAGES = {94--98}, MRCLASS = {65.50 (26.55)}, KEYWORDS = {nls, jacob, inv2}, MRNUMBER = {33 \#5807}, } @article {Ben-Israel66, AUTHOR = {Ben-Israel, A.}, TITLE = {On error bounds for generalized inverses}, JOURNAL = SIAJN, VOLUME = {3}, YEAR = {1966}, PAGES = {585--592}, MRCLASS = {65.35}, KEYWORDS = {pert, invMP}, MRNUMBER = {35 \#6344}, NOTE = {(see also \cite{Stewart69})}, } @article {Ben-Israel66a, AUTHOR = {Ben-Israel, A.}, TITLE = {A {N}ewton-{R}aphson method for the solution of systems of equations}, JOURNAL = JMATA, VOLUME = {15}, YEAR = {1966}, PAGES = {243--252}, MRCLASS = {65.50}, KEYWORDS = {nls, jacob, inv2}, MRNUMBER = {34 \#5273}, } @article {Ben-Israel66b, AUTHOR = {Ben-Israel, A.}, TITLE = {A note on the {C}ayley transform}, JOURNAL = {Notices Amer. Math. Soc.}, VOLUME = {13}, YEAR = {1966}, PAGES = {599}, } @article {Ben-Israel66c, AUTHOR = {Ben-Israel, A.}, TITLE = {A note on an iterative method for generalized inversion of matrices}, JOURNAL = MATHC2, VOLUME = {20}, YEAR = {1966}, PAGES = {439--440}, KEYWORDS = {compit, invMP}, } @article {Ben-Israel67, AUTHOR = {Ben-Israel, A.}, TITLE = {On the geometry of subspaces in {E}uclidean $n$--spaces}, JOURNAL = SIAJA, VOLUME = {15}, YEAR = {1967}, PAGES = {1184--1198}, } @article {Ben-Israel67a, AUTHOR = {Ben-Israel, A.}, TITLE = {On iterative methods for solving nonlinear least squares problems over convex sets}, JOURNAL = ISRJM, VOLUME = {5}, YEAR = {1967}, PAGES = {211--214}, } @inproceedings{Ben-Israel68, AUTHOR = {Ben-Israel, A.}, TITLE = {On applications of generalized inverses in nonlinear analysis}, CROSSREF = {BoullionOdell68}, PAGES = {183--202}, YEAR = {1968}, KEYWORDS = {ana}, } @article {Ben-Israel68a, AUTHOR = {Ben-Israel, A.}, TITLE = {On decompositions of matrix spaces with applications to matrix equations}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {45}, YEAR = {1968}, PAGES = {122--128}, MRCLASS = {15.35}, KEYWORDS = {geos}, MRNUMBER = {40 \#2698}, } @article {Ben-Israel68b, AUTHOR = {Ben-Israel, A.}, TITLE = {On optimal solutions of $2$-person $0$-sum games}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {44}, YEAR = {1968}, PAGES = {512--516}, MRCLASS = {90.70}, MRNUMBER = {39 \#2464}, } @article {Ben-Israel69, AUTHOR = {Ben-Israel, A.}, TITLE = {On matrices of index zero or one}, JOURNAL = SIAJA, VOLUME = {17}, YEAR = {1969}, PAGES = {1118--1121}, MRCLASS = {15.15}, KEYWORDS = {indx}, MRNUMBER = {41 \#5385}, NOTE = {(see \cite{Meyer74}, \cite{Rothblum76})}, } @article {Ben-Israel69a, AUTHOR = {Ben-Israel, A.}, TITLE = {A note on partitioned matrices and equations}, JOURNAL = SIAMR, VOLUME = {11}, YEAR = {1969}, PAGES = {247--250}, MRCLASS = {15.30}, KEYWORDS = {geos, matpar}, MRNUMBER = {39 \#6899}, } @inproceedings {Ben-Israel70, AUTHOR = {Ben-Israel, A.}, TITLE = {On {N}ewton's method in nonlinear programming}, CROSSREF = {Kuhn70}, PAGES = {339--352}, } @inproceedings {Ben-Israel76, AUTHOR = {Ben-Israel, A.}, TITLE = {Applications of generalized inverses to programming, games, and networks}, CROSSREF = {Nashed76}, PAGES = {495--523}, MRCLASS = {90C99 (90B99 90D99)}, KEYWORDS = {app, lp, appnet}, MRNUMBER = {58 \#9304}, } @article {Ben-Israel82, AUTHOR = {Ben-Israel, A.}, TITLE = {A {C}ramer rule for least-norm solutions of consistent linear equations}, JOURNAL = LINAA1, VOLUME = {43}, YEAR = {1982}, PAGES = {223--226}, MRCLASS = {65F20}, MRNUMBER = {83k:65029}, NOTE = {(see \cite{Verghese82}, \cite{ChenY93}, \cite{ChenY93a}, \cite{ChenY93b}, \cite{SunW86}, \cite{WangG86}, \cite{WangG89}, \cite{Werner84})}, } @article {Ben-Israel86, AUTHOR = {Ben-Israel, A.}, TITLE = {Generalized inverses of matrices: a perspective of the work of {P}enrose}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {100}, YEAR = {1986}, NUMBER = {3}, PAGES = {407--425}, MRCLASS = {15A09 (01A60 65F20)}, KEYWORDS = {invMP, his, bibl}, MRNUMBER = {87j:15007}, } @article {Ben-Israel92, AUTHOR = {Ben-Israel, A.}, TITLE = {A volume associated with $m\times n$ matrices}, JOURNAL = LINAA1, VOLUME = {167}, YEAR = {1992}, PAGES = {87--111}, MRCLASS = {15A15 (15A09)}, KEYWORDS = {matvol, svd, algmul, detgen}, MRNUMBER = {93f:15002}, NOTE = {(this concept was introduced by Good \cite{Good80})}, } @article {Ben-Israel99, AUTHOR = {Ben-Israel, A.}, TITLE = {The change-of-variables formula using matrix volume}, JOURNAL = SIAJM1, VOLUME = {21}, YEAR = {1999}, NUMBER = {1}, PAGES = {300--312 (electronic)}, MRCLASS = {15A15 (26B15)}, KEYWORDS = {app, jacob, ana, matvol, appdig, appint}, MRNUMBER = {2000j:15005}, URL = {http://epubs.siam.org/sam%2Dbin/pii.pl?pii=S0895479895296896}, } @article {Ben-Israel00, AUTHOR = {Ben-Israel, A.}, TITLE = {A local inverse for nonlinear mappings}, NOTE = {Mathematical journey through analysis, matrix theory and scientific computation (Kent, OH, 1999)}, JOURNAL = {Numer. Algorithms}, VOLUME = {25}, YEAR = {2000}, NUMBER = {1-4}, PAGES = {37--46}, MRCLASS = {65J15 (15A09 15A15 65F20)}, MRNUMBER = {1 827 144}, KEYWORDS = {Nonlinear operators}, } @ARTICLE{Ben-Israel01, author = {Ben-Israel, A.}, title = {An application of the matrix volume in probability}, journal = LINAA1, year = {2001}, volume = {321}, pages = {9--25}, keywords = {}, } @ARTICLE{Ben-Israel02, author = {Ben-Israel, A.}, title = {The {M}oore of the {M}oore--{P}enrose inverse}, journal = {To appear}, year = {2002}, volume = {}, pages = {}, keywords = {History, Moore}, } @article {Ben-IsraelCharnes63, AUTHOR = {Ben-Israel, A. and Charnes, A.}, TITLE = {Contributions to the theory of generalized inverses}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {11}, YEAR = {1963}, PAGES = {667--699}, MRCLASS = {15.15}, KEYWORDS = {invMP, ana, serexp, spacH}, MRNUMBER = {31 \#3441}, } @article {Ben-IsraelCharnes63a, AUTHOR = {Ben-Israel, A. and Charnes, A.}, TITLE = {Generalized inverses and the {B}ott-{D}uffin network analysis}, JOURNAL = JMATA, VOLUME = {7}, YEAR = {1963}, PAGES = {428--435}, MRCLASS = {15.15}, KEYWORDS = {appnet, invo, geos}, MRNUMBER = {28 \#107}, NOTE = {(corrigendum in {\it J. Math. Anal. Appl.}\ {\bf 18}(1967), 393)}, } @article {Ben-IsraelCharnes68, AUTHOR = {Ben-Israel, A. and Charnes, A.}, TITLE = {An explicit solution of a special class of linear programming problems}, JOURNAL = OPERR1, VOLUME = {16}, YEAR = {1968}, PAGES = {1166--1175}, MRCLASS = {90.50}, KEYWORDS = {lp}, MRNUMBER = {38 \#4137}, NOTE = {(see \cite{Berman79}, \cite{Bilodeau86}, \cite{RobersBen-Israel70}, \cite{Salinetti74})}, } @inproceedings{Ben-IsraeEtAll68, AUTHOR = {Ben-Israel, A. and Charnes, A. and Robers, P. D.}, TITLE = {On generalized inverses and interval linear programming}, CROSSREF = {BoullionOdell68}, PAGES = {53--70}, YEAR = {1968}, } @article {Ben-IsraelCohen66, AUTHOR = {Ben-Israel, A. and Cohen, D.}, TITLE = {On iterative computation of generalized inverses and associated projections}, JOURNAL = SIAJN, VOLUME = {3}, YEAR = {1966}, PAGES = {410--419}, MRCLASS = {65.35}, KEYWORDS = {compit, proj, invMP, serexp}, MRNUMBER = {34 \#3764}, } @book {Ben-IsraelGreville74, AUTHOR = {Ben-Israel, A. and Greville, T. N. E.}, TITLE = {Generalized {I}nverses: {T}heory and {A}pplications}, PUBLISHER = {Wiley-Interscience [John Wiley \& Sons]}, ADDRESS = {New York}, YEAR = {1974}, PAGES = {xi+395}, MRCLASS = {15A09 (47A50 65F20)}, MRNUMBER = {53 \#469}, NOTE = {(reprinted by Robert E. Krieger Publishing Co. Inc., Huntington, NY, 1980.)}, KEYWORDS = {gen, his, bibl}, } @inproceedings {Ben-IsraelGreville76, AUTHOR = {Ben-Israel, A. and Greville, T. N. E.}, TITLE = {Some topics in generalized inverses of matrices}, CROSSREF = {Nashed76}, PAGES = {125--147}, YEAR = {1976}, MRCLASS = {15A09}, KEYWORDS = {gen}, MRNUMBER = {58 \#16714}, } @article {Ben-IsraelKirby69, AUTHOR = {Ben-Israel, A. and Kirby, M. J. L.}, TITLE = {A characterization of equilibrium points of bimatrix games}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {46}, YEAR = {1969}, PAGES = {402--407}, MRCLASS = {90.70}, MRNUMBER = {40 \#8450}, } @article {Ben-IsraelWersan63, AUTHOR = {Ben-Israel, A. and Wersan, S. J.}, TITLE = {An elimination method for computing the generalized inverse of an arbitrary complex matrix}, JOURNAL = JASSC, VOLUME = {10}, YEAR = {1963}, PAGES = {532--537}, MRCLASS = {65.35}, KEYWORDS = {compdi}, MRNUMBER = {31 \#5318}, } @article {BennettEdwards96, AUTHOR = {Bennett, J. M. and Edwards, J. J.}, TITLE = {A graph isomorphism algorithm using pseudoinverses}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {36}, YEAR = {1996}, NUMBER = {1}, PAGES = {41--53}, MRCLASS = {05C60 (05C85 15A09)}, MRNUMBER = {98c:05117}, } @incollection {BensonFrederickson87, AUTHOR = {Benson, M. W. and Frederickson, P. O.}, TITLE = {Fast parallel algorithms for the {M}oore-{P}enrose pseudo-inverse}, BOOKTITLE = {Hypercube {M}ultiprocessors 1987 ({K}noxville, {TN}, 1986)}, PAGES = {597--604}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {1987}, MRCLASS = {65F05 (65W05)}, MRNUMBER = {1 014 275}, KEYWORDS = {compar, invMP}, } @incollection {BensonFrederickson88, AUTHOR = {Benson, M. W. and Frederickson, P. O.}, TITLE = {Fast pseudo-inverse algorithms on hypercubes}, BOOKTITLE = {Multigrid {M}ethods ({C}opper {M}ountain, {CO}, 1987)}, PAGES = {23--33}, PUBLISHER = {Dekker}, ADDRESS = {New York}, YEAR = {1988}, MRCLASS = {65F20 (65W05)}, KEYWORDS = {compar, invMP, mulgr}, MRNUMBER = {89g:65046}, } @article {Ben-TalTeboulle90, AUTHOR = {Ben-Tal, A. and Teboulle, M.}, TITLE = {A geometric property of the least squares solution of linear equations}, JOURNAL = LINAA1, VOLUME = {139}, YEAR = {1990}, PAGES = {165--170}, MRCLASS = {15A06 (90C20)}, MRNUMBER = {91h:15004}, NOTE = {(see \cite{Berg86}, \cite{Dikin74}, \cite{Ben-Israel92}, \cite{Ben-TalTeboulle93}, \cite{BobrovnikovaVavasis00}, \cite{Forsgren96})}, } @article {Ben-TalTeboulle93, AUTHOR = {Ben-Tal, A. and Teboulle, M.}, TITLE = {Addenda: ``{A} geometric property of the least squares solution of linear equations'' [{L}inear {A}lgebra {A}ppl.\ {\bf 139} (1990), 165--170]}, JOURNAL = LINAA1, VOLUME = {180}, YEAR = {1993}, PAGES = {5}, MRCLASS = {15A06 (90C20)}, MRNUMBER = {93k:15004}, } @article {BenziMeyer95, AUTHOR = {Benzi, M. and Meyer, Jr., C. D.}, TITLE = {A direct projection method for sparse linear systems}, JOURNAL = SIAJS1, VOLUME = {16}, YEAR = {1995}, NUMBER = {5}, PAGES = {1159--1176}, MRCLASS = {65F50 (65F05)}, KEYWORDS = {proj}, MRNUMBER = {96j:65043}, } @incollection {BerensFinzel87, AUTHOR = {Berens, H. and Finzel, M.}, TITLE = {A continuous selection of the metric projection in matrix spaces}, BOOKTITLE = {Numerical {M}ethods of {A}pproximation {T}heory, Vol.\ 8 ({O}berwolfach, 1986)}, PAGES = {21--29}, PUBLISHER = {Birkh\"auser}, ADDRESS = {Basel}, YEAR = {1987}, MRCLASS = {41A65 (15A99 41A50 58C06)}, MRNUMBER = {90i:41040}, NOTE = {(see \cite{BerensFinzel90})}, } @article {BerensFinzel90, AUTHOR = {Berens, H. and Finzel, M.}, TITLE = {Addendum: ``{A} continuous selection of the metric projection in matrix spaces'' [in {\it {N}umerical methods of approximation theory, {V}ol.\ 8} ({O}berwolfach, 1986), 21--29, {B}irkh\"auser, {B}asel, 1987; {M}{R} 90i:41040]}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {57}, YEAR = {1990}, NUMBER = {6-7}, PAGES = {663--667}, MRCLASS = {41A65 (15A99 54C65 58C06 65F99)}, MRNUMBER = {91e:41039}, } @BOOK{BerezinZhidkov65, author = {Berezin, I.S. and Zhidkov, N.P.}, title = {Computing {M}ethods}, publisher = {Pergamon Press}, year = {1965}, address = {London}, keywords = {}, } @article {Berg80, AUTHOR = {Berg, L.}, TITLE = {{\"U}ber quasivertauschbare {M}atrixinversen}, JOURNAL = {Rostock. Math. Kolloq.}, FJOURNAL = {Rostocker Mathematisches Kolloquium}, NUMBER = {15}, YEAR = {1980}, PAGES = {5--10}, MRCLASS = {15A09}, MRNUMBER = {82i:15004}, } @article{Berg86, AUTHOR = {Berg, L.}, TITLE = {Three results in connection with inverse matrices}, JOURNAL = LINAA1, VOLUME = {84}, YEAR = {1986}, PAGES = {63--77}, MRCLASS = {15A09 (15A15 15A57)}, MRNUMBER = {88b:15002}, NOTE = {(see also \cite{Ben-TalTeboulle90})}, } @BOOK{BergerGostiaux88, author = {Berger, M. and Gostiaux, B.}, title = {Differential {G}eometry: {M}anifolds, {C}urves and {S}urfaces}, publisher = {Springer-Verlag}, series = {Graduate Texts in Mathematics No. 115}, year = {1988}, address = {New York}, NOTE = {(translated by S. Levy)}, } @article{BergmanEtAl50, author = {P. G. Bergman and R. Penfield and R. Schiller and H. Zatkis}, year = {1950}, title = {The {Hamiltonian} of the General Theory of Relativity with Electromagnetic Field}, journal = {Physical Review}, volume = {52}, pages = {1950}, KEYWORDS = {alglin, apphys}, } @article {Berman74, AUTHOR = {Berman, A.}, TITLE = {Nonnegative matrices which are equal to their generalized inverse}, JOURNAL = LINAA1, VOLUME = {9}, YEAR = {1974}, PAGES = {261--265}, MRCLASS = {15A48}, MRNUMBER = {50 \#4630}, } @article {Berman79, AUTHOR = {Berman, A.}, TITLE = {Generalized interval programming}, JOURNAL = {Bull. Calcutta Math. Soc.}, VOLUME = {71}, YEAR = {1979}, NUMBER = {3}, PAGES = {169--176}, MRCLASS = {90C30}, MRNUMBER = {82a:90130}, } @article {BermanJain88, AUTHOR = {Berman, A. and Jain, S. K.}, TITLE = {Nonnegative generalized inverses of powers of nonnegative matrices}, JOURNAL = LINAA1, VOLUME = {107}, YEAR = {1988}, PAGES = {169--179}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {89g:15006}, } @article {BermanNeumann76, AUTHOR = {Berman, A. and Neumann, M.}, TITLE = {Proper splittings of rectangular matrices}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {31}, YEAR = {1976}, NUMBER = {2}, PAGES = {307--312}, MRCLASS = {15A06 (65F10)}, MRNUMBER = {54 \#330}, } @article {BermanNeumann76a, AUTHOR = {Berman, A. and Neumann, M.}, TITLE = {Consistency and splittings}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {13}, YEAR = {1976}, NUMBER = {6}, PAGES = {877--888}, MRCLASS = {65F10 (93B10)}, MRNUMBER = {55 \#9504}, } @article {BermanPlemmons72, AUTHOR = {Berman, A. and Plemmons, R. J.}, TITLE = {Monotonicity and the generalized inverse}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {22}, YEAR = {1972}, PAGES = {155--161}, MRCLASS = {15A09}, MRNUMBER = {46 \#7254}, } @article {BermanPlemmons74, AUTHOR = {Berman, A. and Plemmons, R. J.}, TITLE = {Inverses of nonnegative matrices}, JOURNAL = LINMA, VOLUME = {2}, YEAR = {1974}, PAGES = {161--172}, MRCLASS = {15A09}, MRNUMBER = {51 \#537}, } @article {BermanPlemmons74a, AUTHOR = {Berman, A. and Plemmons, R. J.}, TITLE = {Cones and iterative methods for best least squares solutions of linear systems}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {11}, YEAR = {1974}, PAGES = {145--154}, MRCLASS = {65F10}, MRNUMBER = {50 \#1478}, } @book {BermanPlemmons94, AUTHOR = {Berman, A. and Plemmons, R. J.}, TITLE = {Nonnegative {M}atrices in the {M}athematical {S}ciences}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1994}, PAGES = {xx+340}, ISBN = {0-89871-321-8}, MRCLASS = {15A48 (15-02 60J10 90C33)}, MRNUMBER = {95e:15013}, NOTE = {(revised reprint of the 1979 original)}, } @ARTICLE{Bernard89, AUTHOR={Bernard, L.}, TITLE={A generalized inverse method for asymptotic linear programming}, JOURNAL={Mathematical Programming}, VOLUME={43}, YEAR={1989}, PAGES={71--86}, } @ARTICLE{Bernard93, AUTHOR={Bernard, L.}, TITLE={An efficient basis update for asymptotic linear programming}, JOURNAL=LINAA1, VOLUME={184}, YEAR={1993}, PAGES={83--102}, } @incollection {BerrymanEtAl90, AUTHOR = {Berryman, Kenneth W. and Inchiosa, Mario E. and Jaffe, Arthur M. and Janowsky, Steven A.}, TITLE = {Extending the pseudoinverse rule}, BOOKTITLE = {Neural {N}etworks and {S}pin {G}lasses (P\^orto Alegre, 1989)}, PAGES = {169--175}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {Teaneck, NJ}, YEAR = {1990}, MRCLASS = {92J40 (92B20)}, MRNUMBER = {92f:92048}, } @article {BerteroEtAl85, AUTHOR = {Bertero, M. and De Mol, C. and Pike, E. R.}, TITLE = {Linear inverse problems with discrete data. {I}. {G}eneral formulation and singular system analysis}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {1}, YEAR = {1985}, NUMBER = {4}, PAGES = {301--330}, MRCLASS = {45E99 (41A15 65J10)}, MRNUMBER = {87e:45005}, } @article {BerteroEtAl88, AUTHOR = {Bertero, M. and De Mol, C. and Pike, E. R.}, TITLE = {Linear inverse problems with discrete data. {I}{I}. {S}tability and regularisation}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {4}, YEAR = {1988}, NUMBER = {3}, PAGES = {573--594}, MRCLASS = {65J10 (47A05 47A50)}, MRNUMBER = {90a:65127}, } @incollection {BerubeEtAl91, AUTHOR = {B{\'e}rub{\'e}, J. and Hartwig, R. E. and Styan, G. P. H.}, TITLE = {On canonical correlations and the degrees of non-orthogonality in the three-way layout}, BOOKTITLE = {Statistical {S}ciences and {D}ata {A}nalysis (Tokyo, 1991)}, PAGES = {247--252}, PUBLISHER = {VSP}, ADDRESS = {Utrecht}, YEAR = {1993}, MRCLASS = {62J05 (62H20)}, KEYWORDS = {appst, geoa}, MRNUMBER = {96m:62117}, } @article {Beutler65a, AUTHOR = {Beutler, F. J.}, TITLE = {The operator theory of the pseudo-inverse. {I}. {B}ounded operators}, JOURNAL = JMATA, VOLUME = {10}, YEAR = {1965}, PAGES = {451--470}, MRCLASS = {47.10}, KEYWORDS = {spacB, spacH, sollsq, solmin, linop}, MRNUMBER = {31 \#3865a}, } @article {Beutler65b, AUTHOR = {Beutler, F. J.}, TITLE = {The operator theory of the pseudo-inverse. {I}{I}. {U}nbounded operators with arbitrary range}, JOURNAL = JMATA, VOLUME = {10}, YEAR = {1965}, PAGES = {471--493}, MRCLASS = {47.10}, KEYWORDS = {spacB, spacH, sollsq, solmin, linop}, MRNUMBER = {31 \#3865b}, } @inproceedings{BeutlerRoot76, AUTHOR = {Beutler, F. J. and Root, W. L.}, TITLE = {The operator pseudoinverse in control and systems identification}, CROSSREF = {Nashed76}, PAGES = {397--494}, YEAR = {1976}, MRCLASS = {93E10 (65F20)}, KEYWORDS = {invMP, spacH, GauMar, appcon}, MRNUMBER = {58 \#9658}, } @article {BevisEtAl81, AUTHOR = {Bevis, J. H. and Hall, F. J. and Katz, I. J.}, TITLE = {Integer generalized inverses of incidence matrices}, JOURNAL = LINAA1, VOLUME = {39}, YEAR = {1981}, PAGES = {247--258}, MRCLASS = {15A09 (05C50)}, MRNUMBER = {82k:15004}, } @article{BevisEtAl87, AUTHOR = {Bevis, J. H. and Hall, F. J. and Hartwig, R. E.}, TITLE = {The {D}razin inverse of a semilinear transformation and its matrix representation}, JOURNAL = LINAA1, VOLUME = {97}, YEAR = {1987}, PAGES = {229--242}, MRCLASS = {15A09 (15A21)}, KEYWORDS = {invD}, MRNUMBER = {88i:15006}, } @incollection {BevisEtAl87a, AUTHOR = {Bevis, J. H. and Hall, F. J. and Hartwig, R. E.}, TITLE = {Consimilarity and the matrix equation ${A}\overline {X}-{X}{B}={C}$}, BOOKTITLE = {Current {T}rends in {M}atrix {T}heory ({A}uburn, {A}la., 1986)}, PAGES = {51--64}, PUBLISHER = {North-Holland}, ADDRESS = {New York}, YEAR = {1987}, MRCLASS = {15A24 (15A21)}, MRNUMBER = {89a:15015}, } @book {Bhatia87, AUTHOR = {Bhatia, R.}, TITLE = {Perturbation {B}ounds for {M}atrix {E}igenvalues}, PUBLISHER = {Longman Scientific \& Technical}, ADDRESS = {Harlow}, YEAR = {1987}, PAGES = {viii+129}, ISBN = {0-582-01379-8}, MRCLASS = {15A42 (15A60 47A55 65F15)}, MRNUMBER = {88k:15020}, } @article {Bhatia91, AUTHOR = {Bhatia, R.}, TITLE = {Letter to the editor: ``{T}he $n$-dimensional {P}ythagorean theorem'' [{L}inear and {M}ultilinear {A}lgebra {\bf 26}(1990), no.\ 1-2, 9--13; {M}{R} 90k:51031] by {S}.-{Y}. {T}. {L}in and {Y}. {F}. {L}in}, JOURNAL = LINMA, VOLUME = {30}, YEAR = {1991}, NUMBER = {1-2}, PAGES = {155}, MRCLASS = {51M05}, MRNUMBER = {1 119 479}, NOTE = {(see \cite{LinLin90})}, } @book {Bhatia97, AUTHOR = {Bhatia, R.}, TITLE = {Matrix {A}nalysis}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xii+347}, ISBN = {0-387-94846-5}, MRCLASS = {15-02 (47-02)}, MRNUMBER = {98i:15003}, } @article {Bhimasankaram74, AUTHOR = {Bhimasankaram, P.}, TITLE = {A characterization of subclasses of generalized inverses of specified rank}, JOURNAL = {Sankhy\=a Ser. A}, VOLUME = {36}, YEAR = {1974}, NUMBER = {2}, PAGES = {214--218}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {52 \#5697}, } @article {Bhimasankaram88, AUTHOR = {Bhimasankaram, P.}, TITLE = {On generalized inverses of a block in a partitioned matrix}, JOURNAL = LINAA1, VOLUME = {109}, YEAR = {1988}, PAGES = {131--143}, MRCLASS = {15A09}, MRNUMBER = {89j:15007}, } @article {Bhimasankaram88a, AUTHOR = {Bhimasankaram, P.}, TITLE = {Rank factorization of a matrix and its applications}, JOURNAL = {Math. Sci.}, FJOURNAL = {The Mathematical Scientist}, VOLUME = {13}, YEAR = {1988}, NUMBER = {1}, PAGES = {4--14}, MRCLASS = {15A23}, MRNUMBER = {90b:15009a}, NOTE = {(see \cite{Rennie88})}, } @article {BhimasankaramMathew93, AUTHOR = {Bhimasankaram, P. and Mathew, T.}, TITLE = {On ordering properties of generalized inverses of nonnegative definite matrices}, JOURNAL = LINAA1, VOLUME = {183}, YEAR = {1993}, PAGES = {131--146}, MRCLASS = {15A09}, MRNUMBER = {93m:15005}, } @article {BhimasankaramSahaRay97, AUTHOR = {Bhimasankaram, P. and SahaRay, R.}, TITLE = {On a partitioned linear model and some associated reduced models}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {264}, YEAR = {1997}, PAGES = {329--339}, MRCLASS = {62J05}, MRNUMBER = {98m:62186}, } @article{Bilodeau86, AUTHOR = {Bilodeau, M.}, TITLE = {Sur une repr{\'e}sentation explicite des solutions optimales d'un programme lin{\'e}aire}, JOURNAL = {Canad. Math. Bull.}, FJOURNAL = {Canadian Mathematical Bulletin}, VOLUME = {29}, YEAR = {1986}, NUMBER = {4}, PAGES = {419--425}, MRCLASS = {90C05 (90C08)}, KEYWORDS = {appopt}, MRNUMBER = {87m:90075}, } @article{Birkhoff11, AUTHOR = {Birkhoff, G. D.}, TITLE = {Review of ``{T}he {N}ew {H}aven {C}olloquium. By {E}. {H}. {M}oore, {E}. {J}. {W}ilczynski, {M}. {M}ason. {Y}ale {U}niversity {P}ress, 1910, x + 222 p.''}, JOURNAL = BULAM1, VOLUME = {17}, YEAR = {1911}, PAGES = {414--428}, KEYWORDS = {History, Moore}, } @book {Birnbaum62, AUTHOR = {Birnbaum, Z. W.}, TITLE = {Introduction to {P}robability and {M}athematical {S}tatistics}, PUBLISHER = {Harper \& Brothers, Publishers, New York}, YEAR = {1962}, PAGES = {viii+325}, MRCLASS = {62.00}, MRNUMBER = {29 \#679}, KEYWORDS = {Probability}, } @ARTICLE{Bjerhammar51, author = {Bjerhammar, A.}, title = {Rectangular reciprocal matrices, with special reference to geodetic calculations}, journal = {Bull. G\'eod\'esique}, year = {1951}, volume = {}, pages = {188--220}, } @article {Bjerhammar51a, AUTHOR = {Bjerhammar, A.}, TITLE = {Application of calculus of matrices to method of least squares with special reference to geodetic calculations}, JOURNAL = {Trans. Roy. Inst. Tech. Stockholm}, VOLUME = {1951}, YEAR = {1951}, NUMBER = {49}, PAGES = {86 pp. (2 plates)}, MRCLASS = {65.0X}, MRNUMBER = {14,1127f}, } @ARTICLE{Bjerhammar58, author = {Bjerhammar, A.}, title = {A generalized matrix algebra}, journal = {Trans. Roy. Inst. Tech. Stockholm}, VOLUME = {1958}, year = {1958}, number = {124}, pages = {32 pp.}, } @article {Bjerhammar67, AUTHOR = {Bjerhammar, A.}, TITLE = {Studies with generalized matrix algebra}, JOURNAL = {Bull. G\'eod\'esique (N.S.) No.}, VOLUME = {85}, YEAR = {1967}, PAGES = {193--210}, MRCLASS = {15.15}, MRNUMBER = {36 \#1459}, } @book {Bjerhammar73, AUTHOR = {Bjerhammar, A.}, TITLE = {Theory of {E}rrors and {G}eneralized {M}atrix {I}nverses}, PUBLISHER = {Elsevier Scientific Publishing Co.}, ADDRESS = {Amsterdam}, YEAR = {1973}, PAGES = {xii+420}, MRCLASS = {62-02 (15A09 65FXX 93E10)}, MRNUMBER = {49 \#1626}, } @ARTICLE{Bjorck67, author = {Bj{\"o}rck, {\AA}.}, title = {Solving linear least squares problems by {G}ram--{S}chmidt orthogonalization}, journal = {BIT}, volume = {7}, year = {1967}, pages = {1--21}, } @ARTICLE{Bjorck67a, author = {Bj{\"o}rck, {\AA}.}, title = {Iterative refinement of linear least squares solutions {I}}, journal = {BIT}, volume = {7}, year = {1967}, pages = {257--278}, } @ARTICLE{Bjorck68, author = {Bj{\"o}rck, {\AA}.}, title = {Iterative refinement of linear least squares solutions {II}}, journal = {BIT}, volume = {8}, year = {1968}, pages = {8--30}, } @incollection {Bjorck74, AUTHOR = {Bj{\"o}rck, {\AA}.}, TITLE = {A uniform numerical method for linear estimation from general {G}auss-{M}arkov models}, BOOKTITLE = {Proceedings of the {F}irst {S}ymposium on {C}omutational {S}tatistics (COMPSTAT), (G. Bruckmann, F. Ferschl and L. Schmetterer, Editors)}, PAGES = {131--140}, PUBLISHER = {Physica Verlag}, YEAR = {1974}, ADDRESS = {Vienna}, } @book {Bjorck94, AUTHOR = {Bj{\"o}rck, {\AA}.}, TITLE = {Numerical {M}ethods for {L}east {S}quares {P}roblems}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1994}, PAGES = {}, ISBN = {}, MRCLASS = {}, MRNUMBER = {}, } @article{BjorckBowie71, author = {Bj{\"o}rck, {\AA}. and Bowie, C.}, year = {1971}, title = {An iterative algorithm for computing the best estimate of an orthogonal matrix}, journal = {SIAJN}, volume = {8}, number = {2}, pages = {358--364}, KEYWORDS = {}, } @article{BjorckElfving79, author = {Bj{\"o}rck, {\AA}. and Elfving, T.}, year = {1979}, title = {Accelerated Projection Methods for Computing Pseudoinverse Solutions of Systems of Linear Equations}, journal = {BIT}, volume = {19}, pages = {145--163}, KEYWORDS = {compit, invMP, lineq}, } @ARTICLE{BjorckGolub67, author = {Bj{\"o}rck, {\AA}. and Golub, G. H.}, title = {Iterative refinement of linear least squares solutions by Householder transformation}, journal = {BIT}, volume = {7}, year = {1967}, pages = {322--337}, } @article{BjorckGolub73, author = {Bj{\"o}rck, {\AA}. and Golub, G. H.}, year = {1973}, title = {Numerical Methods for Computing Angles between Linear Subspaces}, journal = {Mathematics of Computation}, volume = {27}, pages = {579-594}, kwds = {math, nla, gsvd, canonical angles, subspace metric}, } @article {BlaschkeEtAl97, AUTHOR = {Blaschke, B. and Neubauer, A. and Scherzer, O.}, TITLE = {On convergence rates for the iteratively regularized {G}auss-{N}ewton method}, JOURNAL = {IMA J. Numer. Anal.}, FJOURNAL = {IMA Journal of Numerical Analysis}, VOLUME = {17}, YEAR = {1997}, NUMBER = {3}, PAGES = {421--436}, MRCLASS = {65J20 (47H17 65J15)}, MRNUMBER = {98f:65066}, } @article {BlatterCheney72, AUTHOR = {Blatter, J. and Cheney, E. W.}, TITLE = {On the existence of extremal projections}, JOURNAL = {J. Approximation Theory}, VOLUME = {6}, YEAR = {1972}, PAGES = {72--79}, MRCLASS = {41A65}, MRNUMBER = {49 \#3403}, } @ARTICLE{Blattner62, AUTHOR = {Blattner, J. W.}, TITLE = {Bordered matrices}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {10}, YEAR = {1962}, PAGES = {528--536}, MRCLASS = {65.40}, KEYWORDS = {matbor, proj, invMP, eig}, MRNUMBER = {27 \#2098}, } @article {Blattner64, AUTHOR = {Blattner, J. W.}, TITLE = {On the convergence of a certain matrix iteration}, JOURNAL = {Bul. Inst. Politehn. Ia\c si (N.S.)}, VOLUME = {10 (14)}, YEAR = {1964}, NUMBER = {3-4}, PAGES = {43--46}, MRCLASS = {65.35}, KEYWORDS = {matbor, compit}, MRNUMBER = {32 \#1885}, } @ARTICLE{Bliss33, author = {Bliss, G. A.}, title = {Eliakim {H}astings {M}oore}, journal = BULAM1, year = {1933}, volume = {39}, pages = {831--838}, KEYWORDS = {History, Moore}, } @ARTICLE{Bliss34, author = {Bliss, G. A.}, title = {The scientific work of {E}liakim {H}astings {M}oore}, journal = BULAM1, year = {1934}, volume = {40}, pages = {501--514}, KEYWORDS = {History, Moore}, } @preamble{ "\def\polhk#1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} " } @article {BoberChrzan78, AUTHOR = {Bober, L. and Chrzan, P.}, TITLE = {Application of the generalized {M}oore-{P}enrose matrix inversion to the estimation of a classical econometric model under additional constraints}, JOURNAL = {Przegl\polhk ad Statyst.}, FJOURNAL = {Polska Akademia Nauk. Komitet Statistyki i Ekonometrii. Przegl\polhk ad Statystyczny}, VOLUME = {25}, YEAR = {1978}, NUMBER = {3}, PAGES = {315--324 (1979)}, MRCLASS = {62J05}, MRNUMBER = {81b:62080}, } @article {BobrovnikovaVavasis00, AUTHOR = {Bobrovnikova, E. Y. and Vavasis, S. A.}, TITLE = {A norm bound for projections with complex weights}, JOURNAL = LINAA1, VOLUME = {307}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {69--75}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A90}, MRNUMBER = {2000k:15055}, NOTE = {(a complex version of the bounds in \cite{Stewart89}, \cite{Todd90})}, } @article {Boggs76, AUTHOR = {Boggs, P. T.}, TITLE = {The convergence of the {B}en-{I}srael iteration for nonlinear least squares problems}, JOURNAL = {Math. Comp.}, VOLUME = {30}, YEAR = {1976}, NUMBER = {135}, PAGES = {512--522}, MRCLASS = {65K05 (34D20)}, MRNUMBER = {54 \#4095}, } @article {BohlLancaster93, AUTHOR = {Bohl, E. and Lancaster, P.}, TITLE = {Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks}, JOURNAL = LINAA1, VOLUME = {180}, YEAR = {1993}, PAGES = {35--59}, MRCLASS = {34E15 (15A09 34A99 92E20)}, MRNUMBER = {94a:34075}, } @article {BomanKoltracht99, AUTHOR = {Boman, E. and Koltracht, I.}, TITLE = {Computing preconditioners via subspace projection}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {302/303}, YEAR = {1999}, PAGES = {347--353}, MRCLASS = {65F10 (15A12 65F35)}, MRNUMBER = {2000i:65040}, } @ARTICLE{Bohnenblust42, author = {Bohnenblust, F.}, title = {A characterization of complex {H}ilbert spaces}, journal = {Portugal. Math.}, year = {1942}, volume = {3}, pages = {103--109}, } @BOOK{BonnesenFenchel34, author = {Bonnesen, T. and Fenchel, W.}, title = {Theorie der konvexen {K}{\"o}rper}, publisher = {Springer}, year = {1934}, address = {Berlin}, } @PHDTHESIS{deBoor66, author = {Boor, C. de}, title = {The {M}ethod of {P}rojections as applied to the {N}umerical {S}olution of {T}wo {P}oint {B}oundary {V}alue {P}roblems using {C}ubic {S}plines}, school = {University of Michigan}, year = {1966}, type = {Doctoral dissertation in Mathematics}, address = {Ann Arbor, MI}, } @article {deBoor81, AUTHOR = {Boor, C. de}, TITLE = {Convergence of abstract splines}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {31}, YEAR = {1981}, NUMBER = {1}, PAGES = {80--89}, MRCLASS = {41A65 (41A15 41A50)}, MRNUMBER = {82h:41042}, } @article {Boot63, AUTHOR = {Boot, J. C. G.}, TITLE = {The computation of the generalized inverse of singular or rectangular matrices}, JOURNAL = {Amer. Math. Monthly}, VOLUME = {70}, YEAR = {1963}, PAGES = {302--303}, MRCLASS = {15.15}, MRNUMBER = {30 \#104}, } @article {Boros64, AUTHOR = {Boro{\c{s}}, E.}, TITLE = {On the generalized inverse of an ${E}{P}\sb{r}$ matrix}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {2}, YEAR = {1964}, PAGES = {33--38}, MRCLASS = {15.15}, MRNUMBER = {32 \#117}, } @article {Boros65, AUTHOR = {Boro{\c{s}}, E.}, TITLE = {On certain properties of ${E}{P}\sb{r}$ matrices}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {3}, YEAR = {1965}, PAGES = {77--84}, MRCLASS = {15.30}, MRNUMBER = {37 \#2777}, } @article {Boros72, AUTHOR = {Boro{\c{s}}, E.}, TITLE = {Das verallgemeinerte {I}nverse eines linearen {O}perators in {V}ektorr{\"a}umen mit nicht ausgearteter {H}ermitescher {M}etrik {\"u}ber einem kommutativen {K}{\"o}rper}, JOURNAL = {J. Reine Angew. Math.}, VOLUME = {252}, YEAR = {1972}, PAGES = {68--78}, MRCLASS = {15A09}, MRNUMBER = {49 \#2778}, } @article {Boros83, AUTHOR = {Boro{\c{s}}, E.}, TITLE = {The generalized inverse of linear operators on spaces with indefinite metric}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Stiin\c t. Mat.}, FJOURNAL = {Analele Universit\u a\c tii din Timi\c soara. Seria \c Stiin\c te Matematice}, VOLUME = {21}, YEAR = {1983}, NUMBER = {1-2}, PAGES = {9--44}, MRCLASS = {47B50 (47A05)}, MRNUMBER = {85h:47042}, } @article {BorosSturz63, AUTHOR = {Boro{\c{s}}, E. and Sturz, I.}, TITLE = {On quasi-inverse matrices}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {1}, YEAR = {1963}, PAGES = {59--66}, MRCLASS = {15.15}, MRNUMBER = {30 \#2022}, } @article {BoseMitra78, AUTHOR = {Bose, N. K. and Mitra, S. K.}, TITLE = {Generalized inverse of polynomial matrices}, JOURNAL = IEETA5, VOLUME = {23}, YEAR = {1978}, NUMBER = {3}, PAGES = {491--493}, MRCLASS = {15A09 (93B25)}, MRNUMBER = {58 \#22099}, NOTE = {(see also \cite{Sontag80})}, } @article {Bose44, AUTHOR = {Bose, R. C.}, TITLE = {The fundamental theorem of linear estimation (abstract)}, JOURNAL = {Proc. 31st Indian Sci. Congress}, VOLUME = {}, YEAR = {1944}, NUMBER = {}, PAGES = {2--3}, MRCLASS = {}, MRNUMBER = {}, } @ARTICLE{BottDuffin53, author = {Bott, R. and Duffin, R. J.}, title = {On the algebra of networks}, journal = TRAAM, year = {1953}, volume = {74}, pages = {99--109}, } @article {Bouldin73, AUTHOR = {Bouldin, R. H.}, TITLE = {The pseudo-inverse of a product}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {24}, YEAR = {1973}, PAGES = {489--495}, MRCLASS = {47A99}, MRNUMBER = {47 \#5636}, } @article {Bouldin73a, AUTHOR = {Bouldin, R. H.}, TITLE = {The product of operators with closed range}, JOURNAL = {T\^ohoku Math. J. (2)}, VOLUME = {25}, YEAR = {1973}, PAGES = {359--363}, MRCLASS = {47A05}, MRNUMBER = {48 \#4768}, } @article {Bouldin78, AUTHOR = {Bouldin, R. H.}, TITLE = {Selfadjoint approximants}, JOURNAL = {Indiana Univ. Math. J.}, VOLUME = {27}, YEAR = {1978}, NUMBER = {2}, PAGES = {299--307}, MRCLASS = {47B15 (47A55)}, MRNUMBER = {80k:47027}, } @inproceedings{Bouldin82, AUTHOR = {Bouldin, R. H.}, TITLE = {Generalized inverses and factorizations}, CROSSREF = {Campbell82a}, PAGES = {233--249}, YEAR = {1982}, MRCLASS = {47A05 (47A50 47A68)}, KEYWORDS = {spacH, invMP, invD, inv12}, MRNUMBER = {83j:47001}, } @PHDTHESIS{Boullion66, author = {Boullion, T. L.}, title = {Contributions to the {T}heory of {P}seudoinverses}, school = {University of Texas}, year = {1966}, address = {Austin}, } @proceedings{BoullionOdell68, editor = {Boullion, T. L. and Odell, P. L.}, year = {1968}, title = {Proceedings of the {S}ymposium on {T}heory and {A}pplications {G}eneralized {I}nverses of {M}atrices}, publisher = {Texas Tech. Press}, address = {Lubbock}, KEYWORDS = {}, } @article {BoullionOdell69, AUTHOR = {Boullion, T. L. and Odell, P. L.}, TITLE = {A note on the {S}croggs-{O}dell pseudoinverse}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {17}, YEAR = {1969}, PAGES = {7--10}, MRCLASS = {15.15}, MRNUMBER = {39 \#5592}, NOTE = {(correction of \cite[Theorem 6]{ScroggsOdell66})}, } @book{BoullionOdell71, author = {Boullion, T. L. and Odell, P. L.}, year = {1971}, title = {Generalized {I}nverse {M}atrices}, publisher = {John Wiley \& Sons}, address = {New York}, KEYWORDS = {book, alglin, gen}, } @article {BoullionPoole70, AUTHOR = {Boullion, T. L. and Poole, G. D.}, TITLE = {A characterization of the general solution of the matrix equation ${A}{X}+{X}{B}={C}$}, JOURNAL = {Indust. Math.}, VOLUME = {20}, YEAR = {1970}, PAGES = {91--95}, MRCLASS = {15A24}, KEYWORDS = {mateq}, MRNUMBER = {45 \#6839}, } @article {BoulmaaroufEtAl97, AUTHOR = {Boulmaarouf, Z. and Fernandez Miranda, M. and Labrousse, {J-Ph.}}, TITLE = {An algorithmic approach to orthogonal projections and {M}oore-{P}enrose inverses}, JOURNAL = {Numer. Funct. Anal. Optim.}, VOLUME = {18}, YEAR = {1997}, NUMBER = {1-2}, PAGES = {55--63}, MRCLASS = {65J10 (47A05 47A50)}, MRNUMBER = {97m:65105}, } @ARTICLE{Bounitzky09, author = {Bounitzky, E.}, title = {Sur la fonction de {G}reen des {\'e}quations differentielles lin{\'e}aires ordinaires}, journal = {J. Math. Pures Appl.}, year = {1909}, volume = {5}, number = {6}, pages = {65--125}, keywords = {}, } @BOOK{Bourbaki53, author = {Bourbaki, N.}, title = {El{\'e}ments de {M}ath{\'e}matiques. {L}ivre {V}. {E}spaces {V}ectoriels {T}opologiques}, publisher = {Hermann \& Cie}, year = {1953}, address = {Paris}, keywords = {}, } @BOOK{Bourbaki58, author = {Bourbaki, N.}, title = {El{\'e}ments de {M}ath{\'e}matiques. {L}ivre {II}. {A}lg{\`e}bre}, publisher = {Hermann \& Cie}, year = {1958}, address = {Paris}, keywords = {}, } @ARTICLE{BowdlerEtAl66, author = {Bowdler, H. J. and Martin, R. S. and Peters, G. and Wilkinson, J. H.}, title = {Solutions of real and complex systems of linear equations}, journal = NUMEM, year = {1966}, volume = {8}, pages = {217--239}, keywords = {}, NOTE = {(republished, pp. 93--110 in \cite{WilkinsonReinsch71})}, } @ARTICLE{BowmanBurdet74, author = {Bowman, V. J. and Burdet, C.- A.}, title = {On the general solution to systems of mixed--integer linear equations}, journal = SIAJA, year = {1974}, volume = {26}, pages = {120--125}, keywords = {}, } @article {Boyarintsev77, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {General solutions of boundary value problems for singular systems of ordinary differential equations}, JOURNAL = {\v Cisl. Metody Meh. Splo\v sn. Sredy}, VOLUME = {8}, YEAR = {1977}, NUMBER = {7}, PAGES = {12--21}, MRCLASS = {34B05}, MRNUMBER = {58 \#28775}, } @incollection {Boyarintsev78, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {A representation of the {D}razin inverse matrix}, BOOKTITLE = {Numerical {M}ethods of {O}ptimization ({A}pplied {M}athematics) (Russian)}, PAGES = {176--179}, PUBLISHER = {Akad. Nauk SSSR Sibirsk. Otdel. \`Energet. Inst.}, ADDRESS = {Irkutsk}, YEAR = {1978}, MRCLASS = {65F20}, MRNUMBER = {82f:65039}, } @book {Boyarintsev80, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {Regulyarnye i {S}ingulyarnye {S}istemy {L}ineinykh {O}byknovennykh {D}ifferentsialnykh {U}ravnenii}, PUBLISHER = {``Nauka''\ Sibirsk. Otdel.}, ADDRESS = {Novosibirsk}, YEAR = {1980}, PAGES = {223}, MRCLASS = {34A30}, MRNUMBER = {82i:34007}, } @incollection {Boyarintsev82, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {Solving a pair of matrices}, BOOKTITLE = {Approximate {M}ethods for {S}olving {O}perator {E}quations and their {A}pplications}, PAGES = {35--47}, PUBLISHER = {Akad. Nauk SSSR Sibirsk. Otdel. \`Energet. Inst.}, ADDRESS = {Irkutsk}, YEAR = {1982}, MRCLASS = {65F30 (65L99)}, MRNUMBER = {86g:65081}, } @incollection {Boyarintsev83, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {Representation of the solutions of a system of linear algebraic equations by means of generalized inverse matrices}, BOOKTITLE = {Computational {M}ethods in {L}inear {A}lgebra (Russian) (Moscow, 1982)}, PAGES = {33--45}, PUBLISHER = {Akad. Nauk SSSR Otdel Vychisl. Mat.}, ADDRESS = {Moscow}, YEAR = {1983}, MRCLASS = {15A09 (15A06 65F20)}, MRNUMBER = {89b:15004}, } @incollection {Boyarintsev83a, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {The solving pair of matrices and its application}, BOOKTITLE = {Current {P}roblems in {N}umerical and {A}pplied {M}athematics (Novosibirsk, 1981)}, PAGES = {52--55}, PUBLISHER = {``Nauka'' Sibirsk. Otdel.}, ADDRESS = {Novosibirsk}, YEAR = {1983}, MRCLASS = {15A24 (65F30)}, MRNUMBER = {85f:15013}, } @incollection {Boyarintsev86, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {Degenerate systems and the index of a variable matrix}, BOOKTITLE = {Differential {E}quations and {N}umerical {M}ethods}, PAGES = {105--114, 277}, PUBLISHER = {``Nauka'' Sibirsk. Otdel.}, ADDRESS = {Novosibirsk}, YEAR = {1986}, MRCLASS = {34E15}, MRNUMBER = {87m:34070}, } @book {Boyarintsev92, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {Methods of {S}olving {S}ingular {S}ystems of {O}rdinary {D}ifferential {E}quations}, PUBLISHER = {John Wiley \&\ Sons Ltd.}, ADDRESS = {Chichester}, YEAR = {1992}, PAGES = {viii+163}, ISBN = {0-471-93163-2}, MRCLASS = {34A09 (15A09 34A05 34A30 65L12)}, MRNUMBER = {93f:34008}, NOTE = {(translation of the 1988 Russian original)}, } @incollection {Boyarintsev93, AUTHOR = {Boyarintsev, Yu. E.}, TITLE = {A resolving transformation of unknowns in an implicit system of ordinary differential equations}, BOOKTITLE = {Algebrodifferential {S}ystems and {M}ethods for their {S}olution (Russian)}, PAGES = {4--19, 90}, PUBLISHER = {VO ``Nauka''}, ADDRESS = {Novosibirsk}, YEAR = {1993}, MRCLASS = {34A09 (34A30 34C20)}, MRNUMBER = {95a:34003}, } @book {BoyarintsevEtAl89, AUTHOR = {Boyarintsev, Yu. E. and Danilov, V. A. and Loginov, A. A. and Chistyakov, V. F.}, TITLE = {Chislennye {M}etody {R}esheniya {S}ingulyarnykh {S}istem}, PUBLISHER = {``Nauka''\ Sibirsk. Otdel.}, ADDRESS = {Novosibirsk}, YEAR = {1989}, PAGES = {223}, ISBN = {5-02-028735-0}, MRCLASS = {65L99 (65L05)}, MRNUMBER = {91b:65104}, } @incollection {BoyarintsevKorsukov77, AUTHOR = {Boyarintsev, Yu. E. and Korsukov, V. M.}, TITLE = {The structure of a general continuously differentiable solution of a boundary value problem for a singular system of ordinary differential equations}, BOOKTITLE = {Questions in {A}pplied {M}athematics (Russian)}, PAGES = {73--93}, PUBLISHER = {Sibirsk. \`Energet. Inst., Akad. Nauk SSSR Sibirsk. Otdel., Irkutsk}, YEAR = {1977}, MRCLASS = {34B05}, MRNUMBER = {81c:34008}, } @article {BrackxEtAl87, AUTHOR = {Brackx, F. and Delanghe, R. and Van hamme, J.}, TITLE = {Generalized inverses of elliptic systems of differential operators with constant coefficients and related {R}{E}{D}{U}{C}{E} programs for explicit calculations}, JOURNAL = {Rend. Circ. Mat. Palermo (2) Suppl.}, FJOURNAL = {Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento}, NUMBER = {16}, YEAR = {1987}, PAGES = {21--28}, MRCLASS = {35-04 (35J99)}, MRNUMBER = {89f:35004}, } @article {Braden97, AUTHOR = {Braden, H. W.}, TITLE = {${R}$-matrices and generalized inverses}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and General}, VOLUME = {30}, YEAR = {1997}, NUMBER = {15}, PAGES = {L485--L493}, MRCLASS = {58F07 (81R50 81U40)}, MRNUMBER = {98k:58104}, } @article {Braden99, AUTHOR = {Braden, H. W.}, TITLE = {The equations ${A}\sp {T}{X}\pm {X}\sp {T}{A}={B}$}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {20}, YEAR = {1999}, NUMBER = {2}, PAGES = {295--302 (electronic)}, MRCLASS = {15A24 (15A09 58F07 70H05)}, MRNUMBER = {99h:15014}, } @ARTICLE{Bradley66, author = {Bradley, J. S.}, title = {Generalized {G}reen's matrices for compatible differential systems}, journal = {Michigan Math. J.}, year = {1966}, volume = {13}, pages = {97--108}, } @ARTICLE{Bradley66a, author = {Bradley, J. S.}, title = {Adjoint quasi--differential operators of {E}uler type}, journal = PACJM, year = {1966}, volume = {16}, pages = {213--237}, } @ARTICLE{Brand62, author = {Brand, L.}, title = {The solution of linear algebraic equations}, journal = {Math. Gaz.}, year = {1962}, volume = {46}, pages = {203--237}, keywords = {}, } @article {Brezinski97, AUTHOR = {Brezinski, C.}, TITLE = {Projection methods for linear systems}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {77}, YEAR = {1997}, NUMBER = {1-2}, PAGES = {35--51}, MRCLASS = {65F10 (65B05)}, NOTE = {(ROLLS Symposium (Leipzig, 1996))}, MRNUMBER = {97k:65075}, } @article {BrezinskiEtAl94, AUTHOR = {Brezinski, C. and Morandi Cecchi, M. and Redivo Zaglia, M.}, TITLE = {The reverse bordering method}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {15}, YEAR = {1994}, NUMBER = {3}, PAGES = {922--937}, MRCLASS = {65F30 (65B99)}, MRNUMBER = {95b:65061}, } @book {BrezinskiRedivoZaglia91, AUTHOR = {Brezinski, C. and Redivo Zaglia, M.}, TITLE = {Extrapolation {M}ethods. {T}heory and practice, With 1 {IBM-PC} floppy disk (5.25 inch)}, PUBLISHER = {North-Holland Publishing Co.}, ADDRESS = {Amsterdam}, YEAR = {1991}, PAGES = {x+464}, ISBN = {0-444-88814-4}, MRCLASS = {65-02 (65Bxx)}, MRNUMBER = {93d:65001}, } @incollection {BroadbridgePetersen95, AUTHOR = {Broadbridge, P. and Petersen, H. G.}, TITLE = {Use of generalized inverses in the construction of {H}amiltonians for constrained dynamical systems}, BOOKTITLE = {Confronting the {I}nfinite ({A}delaide, 1994)}, PAGES = {307--318}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1995}, MRCLASS = {70F20 (70H05)}, MRNUMBER = {97j:70007}, } @TECHREPORT{denBroederCharnes57, author = {Broeder Jr., C. G. den and Charnes, A.}, title = {Contributions to the theory of generalized inverses for matrices}, institution = {Purdue University}, year = {1957}, type = {Dept. of Math.}, address = {Lafayette, IN}, note = {(Reprinted as ONR Res. Memo. No. 39, Northwestern University, Evanston, IL, 1962)}, } @incollection {BroomheadEtAl87, AUTHOR = {Broomhead, D. S. and Jones, R. and King, G. P. and Pike, E. R.}, TITLE = {Singular system analysis with application to dynamical systems}, BOOKTITLE = {Chaos, {N}oise and {F}ractals ({C}omo, 1986)}, PAGES = {15--27}, PUBLISHER = {Hilger}, ADDRESS = {Bristol}, YEAR = {1987}, MRCLASS = {58F08 (34C30 94A15)}, MRNUMBER = {88m:58087}, } @article {BrownKG78, AUTHOR = {Brown, K. G.}, TITLE = {On ridge estimation in rank deficient models}, JOURNAL = {Comm. Statist. A---Theory Methods}, VOLUME = {7}, YEAR = {1978}, NUMBER = {2}, PAGES = {187--192}, MRCLASS = {}, MRNUMBER = {80a:62108}, } @article {Brown74, AUTHOR = {Brown, R. C.}, TITLE = {Generalized {G}reen's functions and generalized inverses for linear differential systems with {S}tieltjes boundary conditions}, JOURNAL = {J. Differential Equations}, VOLUME = {16}, YEAR = {1974}, PAGES = {335--351}, MRCLASS = {34B10}, MRNUMBER = {50 \#5076}, } @article {BruThome98, AUTHOR = {Bru, R. and Thome, N.}, TITLE = {Group inverse and group involutory matrices}, JOURNAL = LINMA, VOLUME = {45}, YEAR = {1998}, NUMBER = {2-3}, PAGES = {207--218}, MRCLASS = {15A09 (15A23)}, MRNUMBER = {99h:15006}, } @article {Brualdi00, AUTHOR = {Brualdi, R. A.}, TITLE = {From the {E}ditor-in-{C}hief. {C}omment on: ``{T}he explicit solutions and solvability of matrix equations'' [{L}inear {A}lgebra {A}ppl.\ {\bf 311} (2000), no. 1-3, 195--199; {M}{R} 2000m:15019] by {L}. {H}uang}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {320}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {216}, MRCLASS = {15A24}, MRNUMBER = {1 796 552}, } @article {BrualdiSchneider83, AUTHOR = {Brualdi, R. A. and Schneider, H.}, TITLE = {Determinantal identities : {G}auss, {S}chur, {C}auchy, {S}ylvester, {K}ronecker, {J}acobi, {B}inet, {L}aplace, {M}uir and {C}ayley}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {52}, YEAR = {1983}, PAGES = {769--791}, MRCLASS = {}, MRNUMBER = {}, } @incollection {Bruening87, AUTHOR = {Bruening, J. T.}, TITLE = {A new formula for the {M}oore-{P}enrose inverse}, BOOKTITLE = {Current {T}rends in {M}atrix {T}heory ({A}uburn, {A}la., 1986)}, PAGES = {65--74}, PUBLISHER = {North-Holland}, ADDRESS = {New York}, YEAR = {1987}, MRCLASS = {15A09}, MRNUMBER = {88e:15004}, } @article {Bucy94, AUTHOR = {Bucy, R. S.}, TITLE = {Comments on a paper by {F}. {E}. {U}dwadia and {R}. {E}. {K}alaba: ``{A} new perspective on constrained motion'' [{P}roc.\ {R}oy.\ {S}oc.\ {L}ondon {S}er.\ {A} {\bf 439} (1992), no.\ 1906, 407--410; {M}{R} 94b:70027]}, JOURNAL = PRRSLA, VOLUME = {444}, YEAR = {1994}, NUMBER = {1920}, PAGES = {253--255}, MRCLASS = {70H30 (70F99 70H35)}, KEYWORDS = {appcon}, MRNUMBER = {95c:70024}, NOTE = {(see \cite{KalabaUdwadia92})}, } @article {BulutBulut93, AUTHOR = {Bulut, Hamza and Bulut, S. Aysun}, TITLE = {Spectral decompositions and generalized inverses in a circularization network flow problem}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {174}, YEAR = {1993}, PAGES = {390--402}, MRCLASS = {90B10 (15A09 90C35)}, MRNUMBER = {94a:90011}, } @ARTICLE{Burmeister72, author = {Burmeister, W.}, title = {Inversionfreie {V}erfahren zur {L}{\"o}sung nichtlinearer {O}peratorgleichungen}, journal = {Zeit. angew. Math. Mech.}, year = {1972}, volume = {52}, pages = {101--110}, } @ARTICLE{BurnsEtAl74, author = {Burns, F. and Carlson, D. and Haynsworth, E. V. and Markham, T.}, title = {Generalized inverse formulas using the {S}chur complement}, journal = SIAJA, year = {1974}, volume = {26}, pages = {254--259}, KEYWORDS = {Schur complement}, } @ARTICLE{BusingerGolub65, author = {Businger, P. A. and Golub, G. H.}, title = {Linear least squares by {H}ouseholder transformations}, journal = NUMEM, year = {1965}, volume = {7}, pages = {269--276}, NOTE = {(republished, pp. 111--118 in \cite{WilkinsonReinsch71})}, } @ARTICLE{BusingerGolub69, author = {Businger, P. A. and Golub, G. H.}, title = {Algorithm 358: {S}ingular value decomposition of a complex matrix}, journal = COMMA1, year = {1969}, volume = {12}, pages = {564--565}, } @article {ButlerMorley88, AUTHOR = {Butler, C. A. and Morley, T. D.}, TITLE = {A note on the shorted operator}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {9}, YEAR = {1988}, NUMBER = {2}, PAGES = {147--155}, MRCLASS = {15A24 (47B99 94C05)}, MRNUMBER = {89c:15020}, } @article {ButlerMorley88a, AUTHOR = {Butler, C. A. and Morley, T. D.}, TITLE = {Six generalized {S}chur complements}, JOURNAL = LINAA1, VOLUME = {106}, YEAR = {1988}, PAGES = {259--269}, MRCLASS = {15A24 (15A45)}, MRNUMBER = {89h:15022}, } @incollection {Butler74, AUTHOR = {Butler, Kim Ki-Hang}, TITLE = {A {M}oore-{P}enrose inverse for {B}oolean relation matrices}, BOOKTITLE = {Combinatorial {M}athematics ({P}roc. {S}econd {A}ustralian {C}onf., {U}niv. {M}elbourne, {M}elbourne, 1973)}, PAGES = {18--28. Lecture Notes in Math., Vol. 403}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1974}, MRCLASS = {06A40 (15A09)}, MRNUMBER = {50 \#6955}, } @article {Cadzow73, AUTHOR = {Cadzow, J. A.}, TITLE = {A finite algorithm for the minimum $l\sb{\infty }$ solution to a system of consistent linear equations}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {10}, YEAR = {1973}, PAGES = {607--617}, MRCLASS = {65K05 (90C05)}, MRNUMBER = {49 \#6607}, } @article {CallonGroetsch87, AUTHOR = {Callon, G. D. and Groetsch, C. W.}, TITLE = {The method of weighting and approximation of restricted pseudosolutions}, JOURNAL = {J. Approx. Theory}, VOLUME = {51}, YEAR = {1987}, NUMBER = {1}, PAGES = {11--18}, MRCLASS = {65F20 (65J05)}, MRNUMBER = {88j:65079}, } @article {Campbell76, AUTHOR = {Campbell, S. L.}, TITLE = {The {D}razin inverse of an infinite matrix}, JOURNAL = SIAJA, VOLUME = {31}, YEAR = {1976}, NUMBER = {3}, PAGES = {492--503}, MRCLASS = {65F20 (34A35)}, KEYWORDS = {invD, appmar}, MRNUMBER = {55 \#4632}, NOTE = {(see \cite{Campbell82b})}, } @article {Campbell76a, AUTHOR = {Campbell, S. L.}, TITLE = {Differentiation of the {D}razin inverse}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {30}, YEAR = {1976}, NUMBER = {4}, PAGES = {703--707}, MRCLASS = {15A54}, MRNUMBER = {53 \#8101}, } @article {Campbell76b, AUTHOR = {Campbell, S. L.}, TITLE = {Optimal control of autonomous linear processes with singular matrices in the quadratic cost functional}, JOURNAL = {SIAM J. Control Optimization}, VOLUME = {14}, YEAR = {1976}, NUMBER = {6}, PAGES = {1092--1106}, MRCLASS = {93C45 (49B10)}, MRNUMBER = {54 \#12292}, } @article {Campbell77, AUTHOR = {Campbell, S. L.}, TITLE = {Linear systems of differential equations with singular coefficients}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {8}, YEAR = {1977}, NUMBER = {6}, PAGES = {1057--1066}, MRCLASS = {34A30}, MRNUMBER = {57 \#756}, } @article {Campbell77a, AUTHOR = {Campbell, S. L.}, TITLE = {On continuity of the {M}oore-{P}enrose and {D}razin generalized inverses}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {18}, YEAR = {1977}, NUMBER = {1}, PAGES = {53--57}, MRCLASS = {15A09}, MRNUMBER = {58 \#714}, } @article {Campbell78, AUTHOR = {Campbell, S. L.}, TITLE = {Singular perturbation of autonomous linear systems. {I}{I}}, JOURNAL = {J. Differential Equations}, VOLUME = {29}, YEAR = {1978}, NUMBER = {3}, PAGES = {362--373}, MRCLASS = {34E15}, MRNUMBER = {80i:34089b}, } @article {Campbell78a, AUTHOR = {Campbell, S. L.}, TITLE = {Optimal control of discrete linear processes with quadratic cost}, JOURNAL = {Internat. J. Systems Sci.}, VOLUME = {9}, YEAR = {1978}, NUMBER = {8}, PAGES = {841--847}, MRCLASS = {93C55}, MRNUMBER = {58 \#26351}, } @article {Campbell79, AUTHOR = {Campbell, S. L.}, TITLE = {Nonregular singular dynamic {L}eontief systems}, JOURNAL = {Econometrica}, VOLUME = {47}, YEAR = {1979}, NUMBER = {6}, PAGES = {1565--1568}, MRCLASS = {90A16 (15A09)}, MRNUMBER = {80j:90044}, } @article {Campbell79a, AUTHOR = {Campbell, S. L.}, TITLE = {Limit behavior of solutions of singular difference equations}, JOURNAL = LINAA1, VOLUME = {23}, YEAR = {1979}, PAGES = {167--178}, MRCLASS = {93C30 (39A10)}, MRNUMBER = {80c:93066}, } @article {Campbell79b, AUTHOR = {Campbell, S. L.}, TITLE = {Continuity of the {D}razin inverse}, JOURNAL = LINMA, VOLUME = {8}, YEAR = {1979/80}, NUMBER = {3}, PAGES = {265--268}, MRCLASS = {15A09}, MRNUMBER = {81c:15005}, } @article {Campbell79c, AUTHOR = {Campbell, S. L.}, TITLE = {On a singularly perturbed autonomous linear control problem}, JOURNAL = {IEEE Trans. Automat. Control}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control}, VOLUME = {24}, YEAR = {1979}, NUMBER = {1}, PAGES = {115--117}, MRCLASS = {93C99}, MRNUMBER = {80b:93094}, } @book {Campbell80, AUTHOR = {Campbell, S. L.}, TITLE = {Singular {S}ystems of {D}ifferential {E}quations}, PUBLISHER = {Pitman (Advanced Publishing Program)}, ADDRESS = {Boston, Mass.}, YEAR = {1980}, PAGES = {vii+176}, ISBN = {0-8224-8438-2}, MRCLASS = {34-02 (34E15 34H05 93C15)}, MRNUMBER = {81g:34003}, } @article {Campbell81, AUTHOR = {Campbell, S. L.}, TITLE = {On an assumption guaranteeing boundary layer convergence of singularly perturbed systems}, JOURNAL = {Automatica---J. IFAC}, FJOURNAL = {Automatica. The Journal of IFAC. The International Federation of Automatic Control}, VOLUME = {17}, YEAR = {1981}, NUMBER = {4}, PAGES = {645--646}, MRCLASS = {34E10}, MRNUMBER = {83m:34054}, } @proceedings{Campbell82a, EDITOR = {Campbell, S. L.}, YEAR = {1982}, TITLE = {Recent {A}pplications of {G}eneralized {I}nverses}, PUBLISHER = {Pitman (Advanced Publishing Program)}, ADDRESS = {Boston, Mass.}, PAGES = {ii+274}, ISBN = {0-273-08550-6}, MRCLASS = {65-06 (47-06)}, KEYWORDS = {gen, bibl, app}, MRNUMBER = {83h:65010}, } @inproceedings{Campbell82b, AUTHOR = {Campbell, S. L.}, CROSSREF = {Campbell82a}, TITLE = {The {D}razin inverse of an operator}, YEAR = {1982}, PAGES = {250--260}, MRCLASS = {47A50 (34G10 47A05)}, KEYWORDS = {invD, appdif, spacB}, MRNUMBER = {84j:47013}, } @article {Campbell82c, AUTHOR = {Campbell, S. L.}, TITLE = {On positive controllers and linear quadratic optimal control problems}, JOURNAL = {Internat. J. Control}, VOLUME = {36}, YEAR = {1982}, NUMBER = {5}, PAGES = {885--888}, MRCLASS = {49B36}, MRNUMBER = {84h:49049}, } @book {Campbell82d, AUTHOR = {Campbell, S. L.}, TITLE = {Singular {S}ystems of {D}ifferential {E}quations. {I}{I}}, PUBLISHER = {Pitman (Advanced Publishing Program)}, ADDRESS = {Boston, Mass.}, YEAR = {1982}, PAGES = {iii+234}, ISBN = {0-273-08516-6}, MRCLASS = {34-02 (34A08 34E15 93C05)}, MRNUMBER = {84b:34001}, } @article {Campbell83, AUTHOR = {Campbell, S. L.}, TITLE = {Index two linear time-varying singular systems of differential equations}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, VOLUME = {4}, YEAR = {1983}, NUMBER = {2}, PAGES = {237--243}, MRCLASS = {34A08 (15A09)}, MRNUMBER = {84m:34005}, } @article {Campbell88, AUTHOR = {Campbell, S. L.}, TITLE = {Control problem structure and the numerical solution of linear singular systems}, JOURNAL = {Math. Control Signals Systems}, VOLUME = {1}, YEAR = {1988}, NUMBER = {1}, PAGES = {73--87}, MRCLASS = {34H05 (93B40 93C05 93C30)}, MRNUMBER = {89h:34061}, } @article {Campbell92, AUTHOR = {Campbell, S. L.}, TITLE = {Uniqueness of completions for linear time varying differential algebraic equations}, JOURNAL = LINAA1, VOLUME = {161}, YEAR = {1992}, PAGES = {55--67}, MRCLASS = {34A09 (34A30)}, MRNUMBER = {93a:34005}, } @article {Campbell93, AUTHOR = {Campbell, S. L.}, TITLE = {Least squares completions for nonlinear differential algebraic equations}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {65}, YEAR = {1993}, NUMBER = {1}, PAGES = {77--94}, MRCLASS = {65L99 (34A09 34A50)}, MRNUMBER = {94c:65102}, } @article {CampbellMeyer75a, AUTHOR = {Campbell, S. L. and Meyer, Jr., C. D.}, TITLE = {Continuity properties of the {D}razin pseudoinverse}, JOURNAL = LINAA1, VOLUME = {10}, YEAR = {1975}, PAGES = {77--83}, MRCLASS = {15A09}, KEYWORDS = {invD, pert}, MRNUMBER = {51 \#538}, } @article {CampbellMeyer75b, AUTHOR = {Campbell, S. L. and Meyer, Jr., C. D.}, TITLE = {${E}{P}$ operators and generalized inverses}, JOURNAL = {Canad. Math. Bull}, VOLUME = {18}, YEAR = {1975}, NUMBER = {3}, PAGES = {327--333}, MRCLASS = {47A50 (15A09)}, KEYWORDS = {matEP}, MRNUMBER = {53 \#8931}, } @article {CampbellMeyer78, AUTHOR = {Campbell, S. L. and Meyer, Jr., C. D.}, TITLE = {Weak {D}razin inverses}, JOURNAL = LINAA1, VOLUME = {20}, YEAR = {1978}, NUMBER = {2}, PAGES = {167--178}, MRCLASS = {15A09}, KEYWORDS = {invD}, MRNUMBER = {57 \#12546}, } @book {CampbellMeyer79, AUTHOR = {Campbell, S. L. and Meyer, Jr., C. D.}, TITLE = {Generalized {I}nverses of {L}inear {T}ransformations}, PUBLISHER = {Pitman (Advanced Publishing Program)}, ADDRESS = {Boston, Mass.}, YEAR = {1979}, PAGES = {xi+272}, ISBN = {0-273-08422-4}, MRCLASS = {15A09 (65F05)}, KEYWORDS = {gen, his, bibl}, MRNUMBER = {80d:15003}, NOTE = {(reprinted by Dover, 1991)}, } @article {CampbellEtAl76, AUTHOR = {Campbell, S. L. and Meyer, Jr., C. D. and Rose, N. J.}, TITLE = {Applications of the {D}razin inverse to linear systems of differential equations with singular constant coefficients}, JOURNAL = SIAJA, VOLUME = {31}, YEAR = {1976}, NUMBER = {3}, PAGES = {411--425}, MRCLASS = {65F20 (34A05)}, MRNUMBER = {55 \#4633}, KEYWORDS = {invD, diff}, NOTE = {(see \cite{Pandolfi80}, \cite{ChristodoulouParaskevopoulos85}, \cite{GuanEtAl94}, \cite{Wilkinson82})}, } @article {CampbellPoole81, AUTHOR = {Campbell, S. L. and Poole, G. D.}, TITLE = {Convergent regular splittings for nonnegative matrices}, JOURNAL = LINMA, VOLUME = {10}, YEAR = {1981}, NUMBER = {1}, PAGES = {63--73}, MRCLASS = {15A09 (15A48 65F05)}, MRNUMBER = {82m:15005}, } @article {CampbellPoole81a, AUTHOR = {Campbell, S. L. and Poole, G. D.}, TITLE = {Computing nonnegative rank factorizations}, JOURNAL = LINAA1, VOLUME = {35}, YEAR = {1981}, PAGES = {175--182}, MRCLASS = {15A23 (15A09 15A48)}, MRNUMBER = {82f:15009}, } @article {CampbellRakowski94, AUTHOR = {Campbell, S. L. and Rakowski, M.}, TITLE = {Explicit formulae for completions of linear time varying singular systems of differential equations}, JOURNAL = {Circuits Systems Signal Process.}, FJOURNAL = {Circuits, Systems, and Signal Processing}, VOLUME = {13}, YEAR = {1994}, NUMBER = {2-3}, PAGES = {185--199}, MRCLASS = {65L05}, MRNUMBER = {94j:65084}, } @article {CampbellRose78, AUTHOR = {Campbell, S. L. and Rose, N. J.}, TITLE = {Singular perturbation of autonomous linear systems. {I}{I}{I}}, JOURNAL = {Houston J. Math.}, VOLUME = {4}, YEAR = {1978}, NUMBER = {4}, PAGES = {527--539}, MRCLASS = {34E15}, MRNUMBER = {80i:34089c}, } @article {CampbellRose79, AUTHOR = {Campbell, S. L. and Rose, N. J.}, TITLE = {Singular perturbation of autonomous linear systems}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {10}, YEAR = {1979}, NUMBER = {3}, PAGES = {542--551}, MRCLASS = {34E15}, MRNUMBER = {80i:34089a}, } @article {CampbellRose82, AUTHOR = {Campbell, S. L. and Rose, N. J.}, TITLE = {A second order singular linear system arising in electric power systems analysis}, JOURNAL = {Internat. J. Systems Sci.}, VOLUME = {13}, YEAR = {1982}, NUMBER = {1}, PAGES = {101--108}, MRCLASS = {93C05}, MRNUMBER = {84i:93068}, } @article {CampbellYeomans98, AUTHOR = {Campbell, S. L. and Yeomans, K. D.}, TITLE = {Behavior of the nonunique terms in general {D}{A}{E} integrators}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {28}, YEAR = {1998}, NUMBER = {2-4}, PAGES = {209--226}, MRCLASS = {65L05 (65L99)}, MRNUMBER = {99j:65114}, } @article {CaoMa94, AUTHOR = {Cao, Wei Ping and Ma, Ji Pu}, TITLE = {Perturbation of ${A}\sp +\sb 0h$}, JOURNAL = {Numer. Math. J. Chinese Univ. (English Ser.)}, FJOURNAL = {Numerical Mathematics. A Journal of Chinese Universities. (English Series)}, VOLUME = {3}, YEAR = {1994}, NUMBER = {1}, PAGES = {96--103}, MRCLASS = {47A50 (65J10)}, MRNUMBER = {95k:47016}, } @article {CaoMa97, AUTHOR = {Cao, Wei Ping and Ma, Ji Pu}, TITLE = {The pointwise continuity of the {M}-{P} generalized inverses ${A}\sp +\sb x$}, JOURNAL = {Acta Math. Sinica}, VOLUME = {40}, YEAR = {1997}, NUMBER = {2}, PAGES = {287--295}, MRCLASS = {47A05 (45P05 47G10)}, MRNUMBER = {98i:47001}, } @article {CaoMa99, AUTHOR = {Cao, Wei Ping and Ma, Ji Pu}, TITLE = {Moore-{P}enrose generalized inverses of closed operators}, JOURNAL = {Nanjing Daxue Xuebao Shuxue Bannian Kan}, FJOURNAL = {Nanjing Daxue Xuebao. Shuxue Bannian Kan. Nanjing University. Journal. Mathematical Biquarterly}, VOLUME = {16}, YEAR = {1999}, NUMBER = {1}, PAGES = {75--81}, MRNUMBER = {2000d:47002}, } @article {Caradus77, AUTHOR = {Caradus, S. R.}, TITLE = {An equational approach to products of relatively regular operators}, JOURNAL = {Aequationes Math.}, VOLUME = {15}, YEAR = {1977}, NUMBER = {1}, PAGES = {55--62}, MRCLASS = {47A65 (47B35)}, MRNUMBER = {56 \#12945}, } @book {Caradus78, AUTHOR = {Caradus, S. R.}, TITLE = {Generalized {I}nverses and {O}perator {T}heory}, PUBLISHER = {Queen's University}, ADDRESS = {Kingston, Ont.}, YEAR = {1978}, PAGES = {iv+206}, MRCLASS = {47A05 (15A09)}, MRNUMBER = {81m:47003}, } @article {Carlson75, AUTHOR = {Carlson, D.}, TITLE = {Matrix decompositions involving the {S}chur complement}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {28}, YEAR = {1975}, PAGES = {577--587}, MRCLASS = {15A21}, MRNUMBER = {52 \#3189}, } @article {Carlson86, AUTHOR = {Carlson, D.}, TITLE = {What are {S}chur complements, anyway?}, JOURNAL = LINAA1, VOLUME = {74}, YEAR = {1986}, PAGES = {257--275}, MRCLASS = {15A09}, MRNUMBER = {87e:15008}, KEYWORDS = {Schur complement}, } @incollection {Carlson87, AUTHOR = {Carlson, D.}, TITLE = {Generalized inverse invariance, partial orders, and rank-minimization problems for matrices}, BOOKTITLE = {Current {T}rends in {M}atrix {T}heory ({A}uburn, {A}la., 1986)}, PAGES = {81--87}, PUBLISHER = {North-Holland}, ADDRESS = {New York}, YEAR = {1987}, MRCLASS = {15A09 (15A57)}, MRNUMBER = {88f:15006}, } @ARTICLE{CarlsonEtAl74, author = {Carlson, D. and Haynsworth, E. V. and Markham, T.}, title = {A generalization of the {S}chur complement by means of the {M}oore--{P}enrose inverse}, journal = SIAJA, year = {1974}, volume = {26}, pages = {169--175}, KEYWORDS = {Schur complement}, } @TECHREPORT{CaronEtAl99, AUTHOR={Caron, R. and Greenberg, H. J. and Holder, A.}, TITLE={Analytic Centers and Repelling Inequalities}, INSTITUTION={Center for Computational Mathematics}, ADDRESS={University of Colorado at Denver}, NUMBER={CCM 142}, YEAR={1999}, NOTE={(to appear in European Journal of Operations Research)}, } @article {Castro95, AUTHOR = {Castro Gonz{\'a}lez, N.}, TITLE = {On the convergence of semiiterative methods to the {D}razin inverse solution of linear equations in {B}anach spaces}, JOURNAL = {Collect. Math.}, FJOURNAL = {Universitat de Barcelona. Collectanea Mathematica}, VOLUME = {46}, YEAR = {1995}, NUMBER = {3}, PAGES = {303--314}, MRCLASS = {47A50 (47A05 65J10)}, MRNUMBER = {96m:47017}, } @article {CastroKoliha99, AUTHOR = {Castro Gonz{\'a}lez, N. and Koliha, J. J.}, TITLE = {Semi-iterative methods for the {D}razin inverse solution of linear equations in {B}anach spaces}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = {Numerical Functional Analysis and Optimization. An International Journal}, VOLUME = {20}, YEAR = {1999}, NUMBER = {5-6}, PAGES = {405--418}, MRCLASS = {65J10 (47A50 65F10)}, MRNUMBER = {2000h:65074}, } @article {CastroKoliha00, AUTHOR = {Castro Gonz{\'a}lez, N. and Koliha, J. J.}, TITLE = {Perturbation of the {D}razin inverse for closed linear operators}, JOURNAL = {Integral Equations Operator Theory}, VOLUME = {36}, YEAR = {2000}, NUMBER = {1}, PAGES = {92--106}, MRCLASS = {47A05 (34G10 47D06)}, MRNUMBER = {2000j:47001}, } @article {CastroEtAl01, AUTHOR = {Castro Gonz{\'a}lez, N. and Koliha, J. J. and Stra{\v{s}}kraba, I.}, TITLE = {Perturbation of the {D}razin inverse}, JOURNAL = {Soochow J. Math.}, VOLUME = {27}, YEAR = {2001}, NUMBER = {2}, PAGES = {201--211}, MRCLASS = {}, MRNUMBER = {}, } @article {CastroEtAl00, AUTHOR = {Castro Gonz{\'a}lez, N. and Koliha, J. J. and Wei, Yimin}, TITLE = {Perturbation of the {D}razin inverse for matrices with equal eigenprojections at zero}, JOURNAL = LINAA1, VOLUME = {312}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {181--189}, MRCLASS = {15A09}, MRNUMBER = {2001b:15007}, } @book {Catlin89, AUTHOR = {Catlin, D. E.}, TITLE = {Estimation, {C}ontrol, and the {D}iscrete {K}alman {F}ilter}, PUBLISHER = {Springer--Verlag}, ADDRESS = {New York}, YEAR = {1989}, PAGES = {xiii+274}, MRCLASS = {}, MRNUMBER = {}, NOTE = {(see, in particular, pp. 100--113)}, KEYWORDS = {Kalman filter, estimation}, } @article {Cen99, AUTHOR = {Cen, Jian Miao}, TITLE = {Fuzzy matrix partial orderings and generalized inverses}, JOURNAL = {Fuzzy Sets and Systems}, VOLUME = {105}, YEAR = {1999}, NUMBER = {3}, PAGES = {453--458}, } @incollection {ChalmersEtAl00, AUTHOR = {Chalmers, B. L. and Metcalf, F. T. and Shekhtman, B.}, TITLE = {On the computation of minimal projections: millennium report}, BOOKTITLE = {Applied {M}athematics {R}eviews, {V}ol. 1}, PAGES = {119--156}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {2000}, MRCLASS = {41A65 (41A35 46B20 46E30)}, MRNUMBER = {1 782 730}, } @article {Chan95, AUTHOR = {Chan, N. N.}, TITLE = {On a downdating formula for regression}, JOURNAL = {J. Statist. Plann. Inference}, VOLUME = {46}, YEAR = {1995}, NUMBER = {3}, PAGES = {347--350}, MRCLASS = {15A09 (62J05)}, KEYWORDS = {appst, invMP}, MRNUMBER = {96j:15004}, NOTE = {(see \cite{DunneStone93})}, } @inproceedings{Chang82, AUTHOR = {Chang, E.}, TITLE = {The generalized inverse and interpolation theory}, CROSSREF = {Campbell82a}, PAGES = {196--219}, YEAR = {1982}, MRCLASS = {41A10 (47A05)}, KEYWORDS = {spacH, aprx, solmin}, MRNUMBER = {84e:41008}, } @ARTICLE{CharnesCooper68, author = {Charnes, A. and Cooper, W. W.}, title = {Structural sensitivity analysis in linear programming and an exact product form left inverse}, journal = {Naval Res. Logist. Quart.}, year = {1968}, volume = {15}, pages = {517--522}, keywords = {}, } @ARTICLE{CharnesEtAl65, author = {Charnes, A. and Cooper, W. W. and Thompson, G. L.}, title = {Constrained generalized medians and hypermedians as deterministic equivalents for two--stage linear programs under uncertainty}, journal = {Management Sci.}, year = {1965}, volume = {12}, pages = {83--112}, } @TECHREPORT{CharnesGranot73, author = {Charnes, A. and Granot, F.}, title = {Existence and representation of {D}iophantine and mixed {D}iophantine solutions to linear equations and inequalities}, institution = {The University of Texas}, year = {1973}, type = {Center for Cybernetic Studies}, address = {Austin, TX}, } @ARTICLE{CharnesKirby65, author = {Charnes, A. and Kirby, M. J. L.}, title = {Modular design, generalized inverses and convex programming}, journal = OPERR1, year = {1965}, volume = {13}, pages = {836--847}, } @article {ChenG-EtAl96, AUTHOR = {Chen, Guoliang and Wei, Musheng and Xue, Yifeng}, TITLE = {Perturbation analysis of the least squares solution in {H}ilbert spaces}, JOURNAL = LINAA1, VOLUME = {244}, YEAR = {1996}, PAGES = {69--80}, MRCLASS = {47A05 (47A30 47A50 65J10)}, MRNUMBER = {97i:47004}, } @article {ChenG-Wei98, AUTHOR = {Chen, Guoliang and Wei, Yimin}, TITLE = {Perturbation analysis for the projection of a point onto an affine set in a {H}ilbert space}, JOURNAL = {Chinese Ann. Math. Ser. A}, FJOURNAL = {Chinese Annals of Mathematics. Series A. Shuxue Niankan. Ji A}, VOLUME = {19}, YEAR = {1998}, NUMBER = {4}, PAGES = {405--410}, MRCLASS = {49K40 (47A05)}, MRNUMBER = {1 667 326}, NOTE = {(translation in \textit{Chinese J. Contemp. Math.} \textbf{19}(1998), 245--252)}, } @article {ChenG-XueY97, AUTHOR = {Chen, Guoliang and Xue, Yifeng}, TITLE = {Perturbation analysis for the operator equation ${T}x=b$ in {B}anach spaces}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {212}, YEAR = {1997}, NUMBER = {1}, PAGES = {107--125}, MRCLASS = {47A50 (47A05)}, MRNUMBER = {98k:47019}, } @article {ChenG-XueY98, AUTHOR = {Chen, Guoliang and Xue, Yifeng}, TITLE = {The expression of the generalized inverse of the perturbed operator under {T}ype {I} perturbation in {H}ilbert spaces}, JOURNAL = LINAA1, VOLUME = {285}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {1--6}, MRCLASS = {47A05 (47A55 65J10)}, MRNUMBER = {99k:47002}, } @article {Chen82, AUTHOR = {Chen, Han Fu}, TITLE = {Two kinds of linear estimators in {H}ilbert spaces, and their connection}, JOURNAL = {Acta Math. Sinica}, VOLUME = {25}, YEAR = {1982}, NUMBER = {6}, PAGES = {671--679}, MRCLASS = {62J05 (93E10)}, KEYWORDS = {GauMar, spacH}, MRNUMBER = {85c:62157}, } @article {ChenEtAl97, AUTHOR = {Chen, X. and Nashed, M. Z. and Qi, L.}, TITLE = {Convergence of {N}ewton's method for singular smooth and nonsmooth equations using adaptive outer inverses}, JOURNAL = {SIAM J. Optim.}, VOLUME = {7}, YEAR = {1997}, NUMBER = {}, PAGES = {445--462}, MRCLASS = {}, KEYWORDS = {Newton, 2-inverse}, MRNUMBER = {}, } @article {ChenX-Hartwig96, AUTHOR = {Chen, Xuzhou and Hartwig, R. E.}, TITLE = {The hyperpower iteration revisited}, JOURNAL = {Linear Algebra Appl.}, VOLUME = {233}, YEAR = {1996}, PAGES = {207--229}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {97d:15004}, } @article {ChenX-Hartwig96a, AUTHOR = {Chen, Xuzhou and Hartwig, R. E.}, TITLE = {The group inverse of a triangular matrix}, JOURNAL = LINAA1, VOLUME = {237/238}, YEAR = {1996}, PAGES = {97--108}, MRCLASS = {15A09}, KEYWORDS = {invgr}, MRNUMBER = {97a:15008}, } @article {ChenX-Hartwig97, AUTHOR = {Chen, Xuzhou and Hartwig, R. E.}, TITLE = {On the convergence of power scaled {C}es\`aro sums}, JOURNAL = LINAA1, VOLUME = {267}, YEAR = {1997}, PAGES = {335--358}, MRCLASS = {}, MRNUMBER = {98k:15003}, } @article {ChenY83, AUTHOR = {Chen, Yong-Lin}, TITLE = {On the weighted projector and weighted generalized inverse matrices}, JOURNAL = {Acta Math. Appl. Sinica}, VOLUME = {6}, YEAR = {1983}, NUMBER = {3}, PAGES = {282--291}, MRCLASS = {15A09}, MRNUMBER = {85k:15003}, } @article {ChenY90, AUTHOR = {Chen, Yong-Lin}, TITLE = {The generalized {B}ott-{D}uffin inverse and its applications}, JOURNAL = LINAA1, VOLUME = {134}, YEAR = {1990}, PAGES = {71--91}, MRCLASS = {15A09}, MRNUMBER = {91g:15004}, } @article {ChenY93, AUTHOR = {Chen, Yong-Lin}, TITLE = {A {C}ramer rule for solution of the general restricted linear equation}, JOURNAL = LINMA, VOLUME = {34}, YEAR = {1993}, NUMBER = {2}, PAGES = {177--186}, ISSN = {0308-1087}, CODEN = {LNMLAZ}, MRCLASS = {15A06}, MRNUMBER = {96b:15007}, } @article {ChenY93a, AUTHOR = {Chen, Yong-Lin}, TITLE = {Representations and {C}ramer rules for the solution of a restricted matrix equation}, JOURNAL = LINMA, VOLUME = {35}, YEAR = {1993}, NUMBER = {3-4}, PAGES = {339--354}, MRCLASS = {15A24 (15A06)}, MRNUMBER = {96b:15033}, } @article {ChenY93b, AUTHOR = {Chen, Yong-Lin}, TITLE = {An explicit representation of the general solution to a system of constrained linear equations and {C}ramer's rule}, JOURNAL = {Gaoxiao Yingyong Shuxue Xuebao}, FJOURNAL = {Gaoxiao Yingyong Shuxue Xuebao. Applied Mathematics. A Journal of Chinese Universities}, VOLUME = {8}, YEAR = {1993}, NUMBER = {1, Ser. A}, PAGES = {61--70}, MRCLASS = {15A09 (15A06)}, MRNUMBER = {94h:15001}, } @article {ChenY95, AUTHOR = {Chen, Yong-Lin}, TITLE = {Finite algorithms for the $(2)$-generalized inverse ${A}\sp {(2)}\sb {{T},{S}}$}, JOURNAL = LINMA, VOLUME = {40}, YEAR = {1995}, NUMBER = {1}, PAGES = {61--68}, MRCLASS = {15A09}, MRNUMBER = {97a:15009}, } @article {ChenY97, AUTHOR = {Chen, Yong-Lin}, TITLE = {Iterative methods for solving restricted linear equations}, JOURNAL = {Appl. Math. Comput.}, VOLUME = {86}, YEAR = {1997}, NUMBER = {2-3}, PAGES = {171--184}, MRCLASS = {65F10 (15A06)}, MRNUMBER = {98d:65036}, } @article {ChenY00, AUTHOR = {Chen, Yong-Lin}, TITLE = {Defining equations and explicit expressions for the generalized inverse ${A}\sb {{T},{S}}\sp {(2)}$}, JOURNAL = {J. Nanjing Norm. Univ. Nat. Sci. Ed.}, FJOURNAL = {Journal of Nanjing Normal University. Natural Science Edition. Nanjing Shida Xuebao. Ziran Kexue Ban}, VOLUME = {23}, YEAR = {2000}, NUMBER = {2}, PAGES = {5--8}, MRCLASS = {15A09}, MRNUMBER = {2001a:15006}, } @article {ChenY-ChenX00, AUTHOR = {Chen, Yong-Lin and Chen, Xin}, TITLE = {Representation and approximation of the outer inverse ${A}\sp {(2)}\sb {{T},{S}}$ of a matrix ${A}$}, JOURNAL = LINAA1, VOLUME = {308}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {85--107}, MRCLASS = {15A09 (65F10)}, MRNUMBER = {1 751 133}, } @article {ChenY-EtAl95, AUTHOR = {Chen, Yonghong and Kirkland, S. J. and Neumann, M.}, TITLE = {Group generalized inverses of ${M}$-matrices associated with periodic and nonperiodic {J}acobi matrices}, JOURNAL = LINMA, VOLUME = {39}, YEAR = {1995}, NUMBER = {4}, PAGES = {325--340}, MRCLASS = {15A09 (15A51)}, MRNUMBER = {96j:15005}, } @article {ChenY-EtAl96, AUTHOR = {Chen, Yonghong and Kirkland, S. J. and Neumann, M.}, TITLE = {Nonnegative alternating circulants leading to ${M}$-matrix group inverses}, JOURNAL = LINAA1, VOLUME = {233}, YEAR = {1996}, PAGES = {81--97}, MRCLASS = {15A57 (15A09 15A48)}, MRNUMBER = {97h:15031}, } @article {ChenNeumann97, AUTHOR = {Chen, Yonghong and Neumann, M.}, TITLE = {${M}$-matrix generalized inverses of ${M}$-matrices}, JOURNAL = LINAA1, VOLUME = {256}, YEAR = {1997}, PAGES = {263--285}, MRCLASS = {15A09 (15A57)}, MRNUMBER = {97k:15007}, } @article {ChenZK96, AUTHOR = {Chen, Zi Kuan}, TITLE = {Finding the synthetic discriminant function for any sample set by means of the two-step pseudoinverse method}, JOURNAL = {J. Numer. Methods Comput. Appl.}, FJOURNAL = {Journal on Numerical Methods and Computer Applications. Shuxue Jisuan yu Jisuanji Yingyong}, VOLUME = {17}, YEAR = {1996}, NUMBER = {1}, PAGES = {8--13}, MRCLASS = {15A09}, MRNUMBER = {97d:15005}, } @BOOK{Cheney66, author = {Cheney, E. W.}, title = {Introduction to {A}pproximation {T}heory}, publisher = {McGraw--Hill Book Co.}, year = {1966}, address = {New York}, } @ARTICLE{Chernoff53, author = {Chernoff, H.}, title = {Locally optimal designs for estimating parameters}, journal = {Ann. Math. Statist.}, year = {1953}, volume = {24}, pages = {586--602}, } @article {CheverdaKostin95, AUTHOR = {Cheverda, V. A. and Kostin, V. I.}, TITLE = {$r$-pseudoinverses for compact operators in {H}ilbert spaces: existence and stability}, JOURNAL = {J. Inverse Ill-Posed Probl.}, FJOURNAL = {Journal of Inverse and Ill-Posed Problems}, VOLUME = {3}, YEAR = {1995}, NUMBER = {2}, PAGES = {131--148}, ISSN = {0928-0219}, MRCLASS = {47A05 (47A50 47B07 65J10)}, MRNUMBER = {96h:47004}, } @ARTICLE{Chipman64, author = {Chipman, J. S.}, title = {On least squares with insufficient observations}, journal = {J. Amer. Statist. Assoc.}, year = {1964}, volume = {54}, pages = {1078--1111}, keywords = {}, NOTE = {(see \cite{WardEtAl71})}, } @INPROCEEDINGS{Chipman68, author = {Chipman, J. S.}, crossref = {BoullionOdell68}, title = {Specification problems in regression analysis}, year = {1968}, pages = {114--176}, keywords = {}, } @incollection {Chipman97, AUTHOR = {Chipman, J. S.}, TITLE = {``{P}roofs'' and proofs of the {E}ckart-{Y}oung theorem}, BOOKTITLE = {Stochastic {P}rocesses and {F}unctional {A}nalysis ({R}iverside, {CA}, 1994)}, PAGES = {71--83}, PUBLISHER = {Dekker}, ADDRESS = {New York}, YEAR = {1997}, MRCLASS = {15A60 (62J05)}, MRNUMBER = {98k:15037}, } @article {Chipman99, AUTHOR = {Chipman, J. S.}, TITLE = {Linear restrictions, rank reduction, and biased estimation in linear regression}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {55--74}, MRCLASS = {62J07 (62J05 62P20)}, MRNUMBER = {2000j:62106}, } @ARTICLE{ChipmanRao64, author = {Chipman, J. S. and Rao, M. M.}, title = {Projections, generalized inverses and quadratic forms}, journal = JMATA, year = {1964}, volume = {9}, pages = {1--11}, } @ARTICLE{ChipmanRao64a, author = {Chipman, J. S. and Rao, M. M.}, title = {On the treatment of linear restrictions in regression analysis}, journal = {Econometrica}, year = {1964}, volume = {32}, pages = {198--209}, } @article {Chitwood73, AUTHOR = {Chitwood, H.}, TITLE = {Generalized {G}reen's matrices for linear differential systems}, JOURNAL = SIAJM, VOLUME = {4}, YEAR = {1973}, PAGES = {104--110}, MRCLASS = {34B10}, MRNUMBER = {48 \#6524}, } @article {Cho99, AUTHOR = {Cho, Han Hyuk}, TITLE = {Regular fuzzy matrices and fuzzy equations}, JOURNAL = {Fuzzy Sets and Systems}, FJOURNAL = {Fuzzy Sets and Systems. International Journal of Soft Computing and Intelligence}, VOLUME = {105}, YEAR = {1999}, NUMBER = {3}, PAGES = {445--451}, MRCLASS = {15A24 (15A99)}, MRNUMBER = {2000c:15015}, } @article {ChoongKim01, AUTHOR = {Choong, K. K. and Kim, J. -Y.}, TITLE = {A numerical strategy for computing the stability boundaries for multi-loading systems by using generalized inverse and continuation method}, JOURNAL = {Engineering Structures}, VOLUME = {23}, YEAR = {2001}, PAGES = {715--724}, KWDS = {Structural Engineering}, } @article {ChowShen88, AUTHOR = {Chow, Shui-Nee and Shen, Yun Qiu}, TITLE = {Bifurcations via singular value decompositions}, JOURNAL = {Appl. Math. Comput.}, FJOURNAL = {Applied Mathematics and Computation}, VOLUME = {28}, YEAR = {1988}, NUMBER = {3, part I}, PAGES = {231--245}, MRCLASS = {47H15 (65H10 65J15)}, MRNUMBER = {90a:47157}, } @article {Christensen95, AUTHOR = {Christensen, Ole}, TITLE = {Frames and pseudo-inverses}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {195}, YEAR = {1995}, NUMBER = {2}, PAGES = {401--414}, MRCLASS = {47A05}, MRNUMBER = {97c:47003}, } @article {Christensen99, AUTHOR = {Christensen, Ole}, TITLE = {Operators with closed range, pseudo-inverses, and perturbation of frames for a subspace}, JOURNAL = {Canad. Math. Bull.}, VOLUME = {42}, YEAR = {1999}, NUMBER = {1}, PAGES = {37--45}, MRCLASS = {47A05 (42C15 46B15)}, MRNUMBER = {2000d:47003}, } @article {Christensen01, AUTHOR = {Christensen, Ole}, TITLE = {Frames, {R}iesz bases, and discrete {G}abor/Wavelet expansions}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {38}, YEAR = {2001}, NUMBER = {3}, PAGES = {273--291}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Frames, Riesz bases, discrete expansions, Gabor systems, wavelets, frames of exponentials}, } @article {ChristodoulouParaskevopoulos85, AUTHOR = {Christodoulou, M. A. and Paraskevopoulos, P. N.}, TITLE = {Solvability, controllability, and observability of singular systems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {45}, YEAR = {1985}, NUMBER = {1}, PAGES = {53--72}, MRCLASS = {49E15 (93B05)}, MRNUMBER = {86f:49101}, } @article {Chu83, AUTHOR = {Chu, Moody T.}, TITLE = {On a numerical treatment for the curve-tracing of the homotopy method}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {42}, YEAR = {1983}, NUMBER = {3}, PAGES = {323--329}, MRCLASS = {65H10}, MRNUMBER = {85c:65062}, } @article {ChuEtAl97, AUTHOR = {Chu, Moody T. and Funderlic, R. E. and Golub, G. H.}, TITLE = {On a variational formulation of the generalized singular value decomposition}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {18}, YEAR = {1997}, NUMBER = {4}, PAGES = {1082--1092}, MRCLASS = {15A18 (65F15)}, MRNUMBER = {98h:15016}, } @BOOK{Chung74, author = {Chung, Kai Lai}, title = {Elementary {P}robability {T}heory with {S}tochastic {P}rocesses}, publisher = {Springer--Verlag}, year = {1974}, address = {New York}, } @article {Ciecierska98, AUTHOR = {Ciecierska, G.}, TITLE = {A note on another method of computing the {M}oore-{P}enrose inverse of a matrix}, JOURNAL = {Demonstratio Math.}, FJOURNAL = {Demonstratio Mathematica}, VOLUME = {31}, YEAR = {1998}, NUMBER = {4}, PAGES = {879--886}, MRCLASS = {65F20 (15A09 65F15 65F18)}, MRNUMBER = {2000b:65070}, } @article {Cimmino50, AUTHOR = {Cimmino, G.}, TITLE = {Inversione delle corrispondenze funzionali lineari ed equazioni differenziali}, JOURNAL = {Rivista Mat. Univ. Parma}, VOLUME = {1}, YEAR = {1950}, PAGES = {105--116}, MRCLASS = {36.0X}, MRNUMBER = {12,503d}, } @article {Cimmino85, AUTHOR = {Cimmino, G.}, TITLE = {Cramer's rule without the notion of determinant}, JOURNAL = {Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend. (14)}, FJOURNAL = {Atti della Accademia delle Scienze dell'Istituto di Bologna. Classe di Scienze Fisiche. Rendiconti. Serie XIV}, VOLUME = {3}, YEAR = {1985/86}, PAGES = {115--138 (1987)}, MRCLASS = {65F05 (15A06 65C05)}, MRNUMBER = {92a:65089}, } @article {Cimmino86, AUTHOR = {Cimmino, G.}, TITLE = {An unusual way of solving linear systems}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie VIII}, VOLUME = {80}, YEAR = {1986}, NUMBER = {1-2}, PAGES = {6--7 (1987)}, MRCLASS = {15A06 (15A15 65F40)}, MRNUMBER = {89e:15005}, } @article {Cimmino89, AUTHOR = {Cimmino, G.}, TITLE = {On some identities involving spherical means}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie VIII}, VOLUME = {83}, YEAR = {1989}, PAGES = {69--72 (1990)}, MRCLASS = {15A24}, MRNUMBER = {93d:15023}, } @book {Claerbout01, AUTHOR = {Claerbout, J. F.}, TITLE = {Geophysical {E}stimation by {E}xample}, PUBLISHER = {Stanford Exploration Project, Stanford University}, YEAR = {2001}, NOTE = {(on--line book)}, URL = {http://sep.stanford.edu/sep/prof/gee/toc_html/index.html}, } @ARTICLE{Clarkson36, author = {Clarkson, J. A.}, title = {Uniformly convex spaces}, journal = TRAAM, year = {1936}, volume = {40}, pages = {396--414}, } @article {ClimentEtAl97, AUTHOR = {Climent, {J.-J.} and Neumann, M. and Sidi, A.}, TITLE = {A semi-iterative method for real spectrum singular linear systems with an arbitrary index}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {87}, YEAR = {1997}, NUMBER = {1}, PAGES = {21--38}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {99c:65052}, } @article {ClimentEtAl01, AUTHOR = {Climent, {J.-J.} and Thome, N. and Wei, Yimin}, TITLE = {A geometrical approach on generalized inverses by {N}eumann-type series}, BOOKTITLE = {Proceedings of the Eighth Conference of the International Linear Algebra Society (Barcelona, 1999)}, JOURNAL = LINAA1, VOLUME = {332/334}, YEAR = {2001}, PAGES = {533--540}, MRCLASS = {}, MRNUMBER = {1 839 450}, } @ARTICLE{Cline64, author = {Cline, R. E.}, title = {Representations for the generalized inverse of a partitioned matrix}, journal = {J. Soc. Indust. Appl. Math.}, year = {1964}, volume = {12}, pages = {588--600}, } @ARTICLE{Cline65, author = {Cline, R. E.}, title = {Representations for the generalized inverse of sums of matrices}, journal = {J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal.}, year = {1965}, volume = {2}, pages = {99--114}, } @ARTICLE{Cline68, author = {Cline, R. E.}, title = {Inverses of rank invariant powers of a matrix}, journal = SIAJA, year = {1968}, volume = {5}, pages = {182--197}, } @book {Cline79, AUTHOR = {Cline, R. E.}, TITLE = {Elements of the {T}heory of {G}eneralized {I}nverses for {M}atrices. (UMAP modules and monographs in undergraduate mathematics and its applications project). The UMAP Expository Monograph Series)}, PUBLISHER = {EDC/UMAP, Newton, Mass.}, YEAR = {1979}, PAGES = {vi+87}, MRCLASS = {15A09 (15-01 65F20)}, MRNUMBER = {81c:15006}, } @article {Cline81, AUTHOR = {Cline, R. E.}, TITLE = {Note on an extension of the {M}oore-{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {40}, YEAR = {1981}, PAGES = {19--23}, MRCLASS = {15A09 (16A28)}, MRNUMBER = {82i:15005}, } @article {ClineFunderlic79, AUTHOR = {Cline, R. E. and Funderlic, R. E.}, TITLE = {The rank of a difference of matrices and associated generalized inverses}, JOURNAL = LINAA1, VOLUME = {24}, YEAR = {1979}, PAGES = {185--215}, MRCLASS = {15A09 (15A03)}, MRNUMBER = {80f:15004}, } @ARTICLE{ClineGreville70, author = {Cline, R. E. and Greville, T. N. E.}, title = {An extension of the generalized inverse of a matrix}, journal = SIAJA, year = {1970}, volume = {19}, pages = {682--688}, } @article {ClineGreville80, AUTHOR = {Cline, R. E. and Greville, T. N. E.}, TITLE = {A {D}razin inverse for rectangular matrices}, JOURNAL = LINAA1, VOLUME = {29}, YEAR = {1980}, PAGES = {53--62}, MRCLASS = {15A09}, MRNUMBER = {81a:15007}, } @article {ClinePlemmons76, AUTHOR = {Cline, R. E. and Plemmons, R. J.}, TITLE = {$l\sb{2}$-solutions to underdetermined linear systems}, JOURNAL = {SIAM Rev.}, VOLUME = {18}, YEAR = {1976}, NUMBER = {1}, PAGES = {92--106}, MRCLASS = {15-04 (65F05)}, MRNUMBER = {53 \#466}, } @ARTICLE{ClinePyle73, author = {Cline, R. E. and Pyle, L. D.}, title = {The generalized inverse in linear programming. An intersecton projection method and the solution of a class of structured linear programming problems}, journal = SIAJA, year = {1973}, volume = {24}, pages = {338--351}, } @BOOK{CoddingtonLevinson55, author = {Coddington, E. A. and Levinson, N.}, title = {Theory of {O}rdinary {D}ifferential {E}quations}, publisher = {McGraw--Hill Book Co.}, year = {1955}, } @article {Collatz52, AUTHOR = {Collatz, L.}, TITLE = {Aufgaben monotoner {A}rt}, JOURNAL = {Arch. Math.}, VOLUME = {3}, YEAR = {1952}, PAGES = {366--376}, MRCLASS = {65.0X}, MRNUMBER = {14,799h}, } @article {Constales98, AUTHOR = {Constales, D.}, TITLE = {A closed formula for the {M}oore-{P}enrose generalized inverse of a complex matrix of given rank}, JOURNAL = {Acta Math. Hungar.}, VOLUME = {80}, YEAR = {1998}, NUMBER = {1-2}, PAGES = {83--88}, MRCLASS = {15A09}, MRNUMBER = {99e:15001}, KEYWORDS = {invMP}, } @incollection {CorachEtAl01, AUTHOR = {Corach, G. and Maestripieri, A. and Stojanoff, D.}, TITLE = {Generalized orthogonal projections and shorted operators}, BOOKTITLE = {Margarita mathematica}, PAGES = {607--625}, PUBLISHER = {Univ. La Rioja, Logro\~no}, YEAR = {2001}, MRCLASS = {47A64 (46Cxx 47A07)}, MRNUMBER = {1 882 658}, } @article {CorachEtAl01a, AUTHOR = {Corach, G. and Maestripieri, A. and Stojanoff, D.}, TITLE = {Oblique projections and {S}chur complements}, JOURNAL = {Acta Sci. Math. (Szeged)}, FJOURNAL = {Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum}, VOLUME = {67}, YEAR = {2001}, NUMBER = {1-2}, PAGES = {337--356}, MRCLASS = {47Axx (47Bxx)}, MRNUMBER = {1 830 147}, } @article {CorachEtAl02, AUTHOR = {Corach, G. and Maestripieri, A. and Stojanoff, D.}, TITLE = {Generalized {S}chur complements and oblique projections}, JOURNAL = LINAA1, VOLUME = {341}, YEAR = {2002}, NUMBER = {}, PAGES = {259--272}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Schur}, MRNUMBER = {1 873 624}, } @article {CorachPotraEtAl90, AUTHOR = {Corach, G. and Porta, H. and Recht, L.}, TITLE = {Differential geometry of spaces of relatively regular operators}, JOURNAL = {Integral Equations Operator Theory}, FJOURNAL = {Integral Equations and Operator Theory}, VOLUME = {13}, YEAR = {1990}, NUMBER = {6}, PAGES = {771--794}, MRCLASS = {46H99 (46M20 58B20)}, MRNUMBER = {93a:46099}, } @article {Corradi81, AUTHOR = {Corradi, C.}, TITLE = {A note on the solution of separable nonlinear least-squares problems with separable nonlinear equality constraints}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {18}, YEAR = {1981}, NUMBER = {6}, PAGES = {1134--1138}, MRCLASS = {65K05}, MRNUMBER = {82k:65034}, KEYWORDS = {Nonlinear least squares}, } @article {Corradi82, AUTHOR = {Corradi, C.}, TITLE = {Computing methods for restricted estimation in linear models}, JOURNAL = {Statistica (Bologna)}, FJOURNAL = {Statistica}, VOLUME = {42}, YEAR = {1982}, NUMBER = {1}, PAGES = {55--68}, MRCLASS = {62J05 (65F20)}, MRNUMBER = {84a:62093}, NOTE = {(see \cite{GallantGerig80})}, } @article {Cottle74, AUTHOR = {Cottle, R. W.}, TITLE = {Manifestations of the {S}chur complement}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {8}, YEAR = {1974}, PAGES = {189--211}, MRCLASS = {15A21}, MRNUMBER = {50 \#7204}, KEYWORDS = {Schur complement}, } @BOOK{Courant36, author = {Courant, R.}, title = {Differential and {I}ntegral {C}alculus}, publisher = {Interscience Publishers}, year = {1936}, address = {New York}, note = {(translated by E.J. McShane)}, } @BOOK{CourantHilbert53, author = {Courant, R. and Hilbert, D.}, title = {Methods of {M}athematical {P}hysics. {V}ol. {I}}, publisher = {Interscience Publishers}, year = {1953}, address = {New York}, note = {(First published in German 1924)}, } @article {CrabtreeHaynsworth69, AUTHOR = {Crabtree, D. E. and Haynsworth, E. V.}, TITLE = {An identity for the {S}chur complement of a matrix}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {22}, YEAR = {1969}, PAGES = {364--366}, MRCLASS = {15.20}, MRNUMBER = {41 \#234}, KEYWORDS = {Schur complement}, } @incollection {Cudia63, AUTHOR = {Cudia, D. F.}, TITLE = {Rotundity}, BOOKTITLE = {Convexity, {P}roc. {S}ympos. {P}ure {M}ath. {V}ol. {VII} (V. Klee, Editor)}, PAGES = {73--97}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, R.I.}, YEAR = {1963}, } @article {CullenGale65, AUTHOR = {Cullen, C. G. and Gale, K. J.}, TITLE = {A functional definition of the determinant}, JOURNAL = AMEMM, VOLUME = {72}, YEAR = {1965}, PAGES = {403--406}, } @article {Cvetkov55, AUTHOR = {Cvetkov, B.}, TITLE = {A new method of computation in the theory of least squares}, JOURNAL = {Austral. J. Appl. Sci.}, VOLUME = {6}, YEAR = {1955}, PAGES = {274--280}, MRCLASS = {65.0X}, MRNUMBER = {17,301f}, } @article {Dai99, AUTHOR = {Dai, Hua}, TITLE = {An algorithm for symmetric generalized inverse eigenvalue problems}, JOURNAL = LINAA1, VOLUME = {296}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {79--98}, MRCLASS = {65F18 (65F15)}, MRNUMBER = {2000h:65059}, } @Article{DalphinLovass-Nagy73, author = {Dalphin, J. F. and Lovass-Nagy, V.}, title = {Best Least Squares Solutions to Finite Difference Equations Using the Generalized Inverse and Tensor Product Methods}, journal = {Journal of the ACM}, pages = {279--289}, year = {1973}, volume = {20}, number = {2}, keywords = {Moore-Penrose generalized inverse of diagonalizable matrices, tensor product, finite difference approximations, Neumann boundary conditions, direct (non-iterative) techniques, least squares solutions}, } @article {DauxoisNkiet97, AUTHOR = {Dauxois, J. and Nkiet, G. M.}, TITLE = {Canonical analysis of two {E}uclidean subspaces and its applications}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {264}, YEAR = {1997}, PAGES = {355--388}, MRCLASS = {62H20}, MRNUMBER = {99a:62079}, } @article {Davidenko53, AUTHOR = {Davidenko, D. F.}, TITLE = {On a new method of numerical solution of systems of nonlinear equations}, JOURNAL = {Doklady Akad. Nauk SSSR (N.S.)}, VOLUME = {88}, YEAR = {1953}, PAGES = {601--602}, MRCLASS = {65.0X}, MRNUMBER = {14,906f}, } @article {Davidenko60, AUTHOR = {Davidenko, D. F.}, TITLE = {The method of variation of parameters as applied to the computation of eigenvalues and eigenvectors of matrices}, JOURNAL = {Soviet Math. Dokl.}, VOLUME = {1}, YEAR = {1960}, PAGES = {364--367}, MRCLASS = {65.00}, MRNUMBER = {22 \#10164c}, } @article {Davidenko60a, AUTHOR = {Davidenko, D. F.}, TITLE = {The evaluation of determinants by the method of variation of parameters}, JOURNAL = {Soviet Math. Dokl.}, VOLUME = {1}, YEAR = {1960}, PAGES = {316--319}, MRCLASS = {65.00}, MRNUMBER = {22 \#10164b}, } @article {Davidenko60b, AUTHOR = {Davidenko, D. F.}, TITLE = {Inversion of matrices by the method of variation of parameters}, JOURNAL = {Soviet Math. Dokl.}, VOLUME = {1}, YEAR = {1960}, PAGES = {279--282}, MRCLASS = {65.00}, MRNUMBER = {22 \#10164a}, } @incollection {Davidenko88, AUTHOR = {Davidenko, D. F.}, TITLE = {Pseudo-inversion and construction of generalized solutions of linear equations that arise in calculations for nuclear reactors}, BOOKTITLE = {Computational {P}rocesses and {S}ystems, {N}o.\ 6 (Russian)}, PAGES = {98--109}, PUBLISHER = {``Nauka''}, ADDRESS = {Moscow}, YEAR = {1988}, MRCLASS = {65J05 (47A50 65L05)}, MRNUMBER = {90h:65087}, } @article {Davis58, AUTHOR = {Davis, C.}, TITLE = {Separation of two linear subspaces}, JOURNAL = {Acta Sci. Math. Szeged}, VOLUME = {19}, YEAR = {1958}, PAGES = {172--187}, MRCLASS = {46.00}, MRNUMBER = {20 \#5425}, } @incollection {Davis88, AUTHOR = {Davis, C.}, TITLE = {Completing a matrix so as to minimize the rank}, BOOKTITLE = {Topics in {O}perator {T}heory and {I}nterpolation}, PAGES = {87--95}, PUBLISHER = {Birkh{\"a}user}, ADDRESS = {Basel}, YEAR = {1988}, MRCLASS = {47A20 (15A03)}, MRNUMBER = {89d:47010}, } @article {DavisKahan69, AUTHOR = {Davis, C. and Kahan, W. M.}, TITLE = {Some new bounds on perturbation of subspaces}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {75}, YEAR = {1969}, PAGES = {863--868}, MRCLASS = {47.48}, MRNUMBER = {39 \#7460}, } @article {DavisKahan70, AUTHOR = {Davis, C. and Kahan, W. M.}, TITLE = {The rotation of eigenvectors by a perturbation. {III}}, JOURNAL = SIAJN, VOLUME = {7}, YEAR = {1970}, PAGES = {1--46}, MRCLASS = {}, MRNUMBER = {}, } @ARTICLE{DavisRobinson72, author = {Davis, D. L. and Robinson, D. W.}, title = {Generalized inverses of morphisms}, journal = LINAA1, year = {1972}, volume = {5}, pages = {329--338}, } @article {DeanPorrill98, AUTHOR = {Dean, P. and Porrill, J.}, TITLE = {Pseudo-inverse control in biological systems: a learning mechanism for fixation stability}, JOURNAL = {Neural Networks}, VOLUME = {11}, YEAR = {1998}, PAGES = {1205--1218}, } @book {Deans93, AUTHOR = {Deans, S. R.}, TITLE = {The {R}adon {T}ransform and some of its {A}pplications (Revised reprint of the 1983 original)}, PUBLISHER = {Robert E. Krieger Publishing Co. Inc.}, ADDRESS = {Malabar, FL}, YEAR = {1993}, PAGES = {xii+295}, ISBN = {0-89464-718-0}, MRCLASS = {44A12 (44-02)}, MRNUMBER = {95a:44003}, } @article {Decell65, AUTHOR = {Decell, Jr., H. P.}, TITLE = {An alternate form of the generalized inverse of an arbitrary complex matrix}, JOURNAL = SIAMR, VOLUME = {7}, YEAR = {1965}, PAGES = {356--358}, MRCLASS = {15.15}, KEYWORDS = {invMP, inv1, repcl}, MRNUMBER = {32 \#1213}, NOTE = {(see \cite{Zlobec70})}, } @article {Decell65a, AUTHOR = {Decell, Jr., H. P.}, TITLE = {An application of the {C}ayley-{H}amilton theorem to generalized matrix inversion}, JOURNAL = SIAMR, VOLUME = {7}, YEAR = {1965}, PAGES = {526--528}, MRCLASS = {15.15}, MRNUMBER = {33 \#2656}, NOTE = {(extended in \cite{WangG87})}, } @article {Decell73, AUTHOR = {Decell, Jr., H. P.}, TITLE = {On the derivative of the generalized inverse of a matrix}, JOURNAL = LINMA, VOLUME = {1}, YEAR = {1973/74}, PAGES = {357--359}, MRCLASS = {15A09}, MRNUMBER = {49 \#5026}, KEYWORDS = {matder, pert, invMP}, } @article {DecellOdell67, AUTHOR = {Decell, Jr., H. P. and Odell, P. L.}, TITLE = {On the fixed point probability vector of regular or ergodic transition matrices}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {62}, YEAR = {1967}, PAGES = {600--602}, MRCLASS = {60.65 (15.00)}, MRNUMBER = {36 \#972}, } @article {DecellWiginton68, AUTHOR = {Decell, Jr., H. P. and Wiginton, C. L.}, TITLE = {A characterization of the maximal subgroups of the semigroup of $n\times n$ complex matrices}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {18 (93)}, YEAR = {1968}, PAGES = {675--677}, MRCLASS = {20.92}, MRNUMBER = {38 \#3366}, } @article {Dederick13, AUTHOR = {Dederick, L. S.}, TITLE = {On the character of a transformation in the neighborhood of a point where its {J}acobian vanishes}, JOURNAL = TRAAM, VOLUME = {14}, YEAR = {1913}, PAGES = {143--148}, KEYWORDS = {Jacobian, singular point}, } @article {DedieuShub00, AUTHOR = {Dedieu, J. P. and Shub, M.}, TITLE = {Newton's method for overdetermined systems of equations}, JOURNAL = {Math. of Comput.}, VOLUME = {69}, YEAR = {2000}, PAGES = {1099--1115}, MRCLASS = {}, MRNUMBER = {}, } @article {DeLathauwerEtAl00, AUTHOR = {De Lathauwer, L. and De Moor, B. and Vanderwalle, J.}, TITLE = {A multilinear singular value decomposition}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {21}, YEAR = {2000}, NUMBER = {4}, PAGES = {1253--1278 (electronic)}, ISSN = {1095-7162}, MRCLASS = {15A69 (15A18 65F30)}, MRNUMBER = {2001f:15031}, KEYWORDS = {SVD, tensors}, } @article {DeLathauwerEtAl00a, AUTHOR = {De Lathauwer, L. and De Moor, B. and Vanderwalle, J.}, TITLE = {On the best rank-1 and rank-$({R}\sb 1,{R}\sb 2,\cdots,{R}\sb{N})$ approximation of higher-order tensors}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {21}, YEAR = {2000}, NUMBER = {4}, PAGES = {1324--1342 (electronic)}, ISSN = {1095-7162}, MRCLASS = {15A69 (65F30)}, MRNUMBER = {1 780 276}, KEYWORDS = {Best rank approximation, SVD, tensors}, } @article {Delvos78, AUTHOR = {Delvos, F. {-J.}}, TITLE = {Splines and pseudo-inverses}, JOURNAL = {RAIRO Anal. Num\'er.}, FJOURNAL = {RAIRO Analyse Num\'erique}, VOLUME = {12}, YEAR = {1978}, NUMBER = {4}, PAGES = {313--324, v}, MRCLASS = {65J10 (41A15 47A50)}, MRNUMBER = {80a:65118}, } @article {Delvos87, AUTHOR = {Delvos, F. {-J}. and Schempp, W.}, TITLE = {Convergence of approximate splines via pseudo-inverses}, JOURNAL = {RAIRO Mod\'el. Math. Anal. Num\'er.}, FJOURNAL = {RAIRO Mod\'elisation Math\'ematique et Analyse Num\'erique}, VOLUME = {21}, YEAR = {1987}, NUMBER = {2}, PAGES = {261--267}, MRCLASS = {65J05 (41A15 65D07)}, MRNUMBER = {88g:65056}, } @article {DeMeersman70, AUTHOR = {de Meersman, R.}, TITLE = {Geometric meaning of the method of {G}olub and {K}ahan for the calculation of the singular values of a matrix}, JOURNAL = {Bull. Soc. Math. Belg.}, VOLUME = {22}, YEAR = {1970}, PAGES = {146--154}, MRCLASS = {65.40}, MRNUMBER = {43 \#7053}, } @article {DeMeersman71, AUTHOR = {De Meersman, R.}, TITLE = {Algorithms for pseudo-inverses of linear mappings. {A} unified approach}, JOURNAL = {Bull. Soc. Math. Belg.}, VOLUME = {23}, YEAR = {1971}, PAGES = {283--294}, MRCLASS = {15A09 (65F05)}, MRNUMBER = {46 \#7255}, } @article {DeMeersmanSiau77, AUTHOR = {De Meersman, R. and Siau, P.}, TITLE = {On updating formulas for least squares solutions and pseudo-inverses}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {3}, YEAR = {1977}, NUMBER = {4}, PAGES = {293--297}, MRCLASS = {65F20}, MRNUMBER = {57 \#1851}, } @article {DeMoor93, AUTHOR = {De Moor, B.}, TITLE = {Structured total least squares and $L_2$ approximation problems}, JOURNAL = LINAA1, VOLUME = {188/189}, YEAR = {1993}, NUMBER = {}, PAGES = {163--205}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {TLS}, } @BOOK{Dennis59, author = {Dennis, J. B.}, title = {Mathematical {P}rogramming and {E}lectrical {N}etworks}, publisher = {MIT Press}, year = {1959}, address = {Cambridge, Mass.}, } @article {DentNewhouse59, AUTHOR = {Dent, B. A. and Newhouse, A.}, TITLE = {Polynomials orthogonal over discrete domains}, JOURNAL = SIAMR, VOLUME = {1}, YEAR = {1959}, PAGES = {55--59}, MRCLASS = {65.00 (41.00)}, MRNUMBER = {20 \#6773}, } @article {DePierroWeiM98, AUTHOR = {De Pierro, A. R. and Wei, Musheng}, TITLE = {Reverse order law for reflexive generalized inverses of products of matrices}, JOURNAL = LINAA1, VOLUME = {277}, YEAR = {1998}, PAGES = {299--311}, MRCLASS = {15A09 (15A23)}, MRNUMBER = {99e:15002}, } @article {DePierroWeiM00, AUTHOR = {De Pierro, A. R. and Wei, Musheng}, TITLE = {Some new properties of the equality constrained and weighted least squares problem}, JOURNAL = LINAA1, VOLUME = {320}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {145--165}, MRCLASS = {65K05 (15A23 90C20)}, MRNUMBER = {1 795 724}, } @article {DesoerWhalen63, AUTHOR = {Desoer, C. A. and Whalen, B. H.}, TITLE = {A note on pseudoinverses}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {11}, YEAR = {1963}, PAGES = {442--447}, MRCLASS = {47.10}, MRNUMBER = {27 \#6128}, KEYWORDS = {spacH, invMP}, } @article {Desplas92, AUTHOR = {Desplas, M.}, TITLE = {Matrice pseudo-inverse de {M}oore-{P}enrose et variables duales g\'en\'eralis\'ees en programmation math\'ematique}, JOURNAL = {RAIRO Rech. Op\'er.}, FJOURNAL = {RAIRO Recherche Op\'erationnelle}, VOLUME = {26}, YEAR = {1992}, NUMBER = {4}, PAGES = {313--360}, MRCLASS = {90C30 (49N15 90A40 90C31)}, MRNUMBER = {93j:90096}, } @article {Deuflhard74, AUTHOR = {Deuflhard, P.}, TITLE = {A modified {N}ewton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting}, JOURNAL = {Numer. Math.}, VOLUME = {22}, YEAR = {1974}, PAGES = {289--315}, MRCLASS = {65L10}, MRNUMBER = {50 \#3584}, } @article {DeuflhardHeindl79, AUTHOR = {Deuflhard, P. and Heindl, G.}, TITLE = {Affine invariant convergence theorems for {N}ewton's method and extensions to related methods}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {16}, YEAR = {1979}, PAGES = {1--10}, MRCLASS = {}, MRNUMBER = {}, } @article {DeuflhardSautter80, AUTHOR = {Deuflhard, P. and Sautter, W.}, TITLE = {On rank-deficient pseudoinverses}, JOURNAL = LINAA1, VOLUME = {29}, YEAR = {1980}, PAGES = {91--111}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {81g:65049}, } @ARTICLE{Deutsch71, author = {Deutsch, E.}, title = {Semi--inverses, reflexive semi--inverses, and pseudo--inverses of an arbitrary linear transformation}, journal = LINAA1, year = {1971}, volume = {4}, pages = {313--322}, } @article {DeutschNeumann84, AUTHOR = {Deutsch, E. and Neumann, M.}, TITLE = {Derivatives of the {P}erron root at an essentially nonnegative matrix and the group inverse of an ${M}$-matrix}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {102}, YEAR = {1984}, NUMBER = {1}, PAGES = {1--29}, MRCLASS = {15A48}, MRNUMBER = {85h:15023}, } @incollection {Deutsch95, AUTHOR = {Deutsch, F.}, TITLE = {The angle between subspaces of a {H}ilbert space}, BOOKTITLE = {Approximation {T}heory, {W}avelets and {A}pplications ({M}aratea, 1994)}, PAGES = {107--130}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1995}, MRCLASS = {46C05 (47A05 65J05)}, MRNUMBER = {96e:46027}, } @book {Deutsch01, AUTHOR = {Deutsch, F.}, TITLE = {Best {A}pproximation in {I}nner {P}roduct {S}paces}, PUBLISHER = {Springer--Verlag}, ADDRESS = {New York}, YEAR = {2001}, MRCLASS = {}, MRNUMBER = {}, } @Article{DeVelKrishnamurthy88, author = {{De Vel}, O. Y. and Krishnamurthy, E. V.}, title = {An iterative pipelined array architecture for the generalized matrix inversion}, journal = {Information Processing Letters}, volume = {26}, number = {5}, pages = {263--267}, year = {1988}, mrclass = {65F20 (65V05 65W05)}, mrnumber = {88j:65080}, } @article {DiazLozano98, AUTHOR = {D{\'\i}az Lozano, M. E.}, TITLE = {The class of $\{1,2,4\}$-inverses as the solution of a linear problem}, JOURNAL = {Bol. Soc. Mat. Mexicana (3)}, FJOURNAL = {Sociedad Matem\'atica Mexicana. Bolet\'\i n. Tercera Serie}, VOLUME = {4}, YEAR = {1998}, NUMBER = {2}, PAGES = {223--228}, MRCLASS = {15A09 (15A04 15A06)}, MRNUMBER = {99j:15007}, } @article{DidenkoSilbermann98, AUTHOR = {Didenko, V. D. and Silbermann, B.}, TITLE = {Extension of ${C}\sp *$-algebras and {M}oore-{P}enrose stability of sequences of additive operators}, JOURNAL = LINAA1, VOLUME = {275/276}, YEAR = {1998}, PAGES = {121--140}, MRCLASS = {46L99 (45E05 45L05 47A50 47G10)}, MRNUMBER = {99e:46095}, KEYWORDS = {Moore-Penrose, additive operators, spline approximation}, } @article {DieleEtAl98, AUTHOR = {Diele, F. and Lopez, L. and Peluso, R.}, TITLE = {The {C}ayley transform in the numerical solution of unitary differential systems}, JOURNAL = {Adv. Comput. Math.}, FJOURNAL = {Advances in Computational Mathematics}, VOLUME = {8}, YEAR = {1998}, NUMBER = {4}, PAGES = {317--334}, MRCLASS = {65L99}, MRNUMBER = {99f:65123}, } @Article{Dikin74, author = {Dikin, I. I.}, title = {On the speed of an iterative process}, journal = {Upravlyaemye Sistemi}, year = {1974}, volume = {12}, pages = {54--60}, NOTE = {(see \cite{VanderbeiLagarias90})}, } @article {Dines19, AUTHOR = {Dines, L. L.}, TITLE = {Projective transformations in function space}, JOURNAL = TRAAM, VOLUME = {20}, YEAR = {1919}, PAGES = {45--65}, NOTE = {(see p. 403 and \cite{Hildebrandt20})}, } @article {Ding98, AUTHOR = {Ding, Jiu}, TITLE = {Perturbation results for projecting a point onto a linear manifold}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {19}, YEAR = {1998}, NUMBER = {3}, PAGES = {696--700 (electronic)}, ISSN = {1095-7162}, MRCLASS = {15A09 (15A12 65F20)}, MRNUMBER = {99e:15003}, } @article {Ding00, AUTHOR = {Ding, Jiu}, TITLE = {Perturbation of systems of linear algebraic equations}, JOURNAL = {Linear and Multilinear Algebra}, VOLUME = {47}, YEAR = {2000}, NUMBER = {2}, PAGES = {119--127}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {2001a:65045}, } @article {Ding01, AUTHOR = {Ding, Jiu}, TITLE = {Lower and upper bounds in the perturbation of general linear algebraic equations}, JOURNAL = {Appl. Math. Lett.}, FJOURNAL = {Applied Mathematics Letters. An International Journal of Rapid Publication}, VOLUME = {14}, YEAR = {2001}, NUMBER = {1}, PAGES = {49--52}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {1 793 702}, } @article{DingHuang94, AUTHOR = {Ding, Jiu and Huang, Liang Jiao}, TITLE = {On the perturbation of the least squares solutions in {H}ilbert spaces}, JOURNAL = LINAA1, VOLUME = {212/213}, YEAR = {1994}, PAGES = {487--500}, MRCLASS = {47A55 (47A05 65J99)}, MRNUMBER = {95i:47023}, } @article {DingHuang96, AUTHOR = {Ding, Jiu and Huang, Liang Jiao}, TITLE = {Perturbation of generalized inverses of linear operators in {H}ilbert spaces}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {198}, YEAR = {1996}, NUMBER = {2}, PAGES = {506--515}, MRCLASS = {47A50 (47A05 47A55)}, MRNUMBER = {97i:47017}, } @article {DingHuang97, AUTHOR = {Ding, Jiu and Huang, Liang Jiao}, TITLE = {On the continuity of generalized inverses of linear operators in {H}ilbert spaces}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {262}, YEAR = {1997}, PAGES = {229--242}, MRCLASS = {47A05 (47A50)}, MRNUMBER = {98k:47002}, } @article {DjordjevicStanimirovic98, AUTHOR = {Djordjevi{\'c}, D. S. and Stanimirovi{\'c}, P. S.}, TITLE = {Universal iterative methods for computing generalized inverses}, JOURNAL = {Acta Math. Hungar.}, VOLUME = {79}, YEAR = {1998}, NUMBER = {3}, PAGES = {253--268}, MRCLASS = {15A09}, MRNUMBER = {99c:15006}, KEYWORDS = {detgen, compex, invo}, } @article {DjordjevicStanimirovic00, AUTHOR = {Djordjevi{\'c}, D. S. and Stanimirovi{\'c}, P. S.}, TITLE = {Applications of the {G}roetsch theorem}, JOURNAL = {Indian J. Pure Appl. Math.}, VOLUME = {31}, YEAR = {2000}, NUMBER = {3}, PAGES = {277--286}, MRCLASS = {47A05}, MRNUMBER = {1 754 497}, } @article {Dobovisek01, AUTHOR = {Dobovi{\v{s}}ek, M.}, TITLE = {On minimal solutions of the matrix equation ${A}{X}-{Y}{B}=0$}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {325}, YEAR = {2001}, NUMBER = {1-3}, PAGES = {81--99}, MRCLASS = {15A24}, MRNUMBER = {1 810 097}, } @article {Dokovic65, AUTHOR = {Dokovi{\'c}, Dragomir {\v{Z}}.}, TITLE = {On the generalized inverse for matrices}, JOURNAL = {Glasnik Mat.-Fiz. Astronom. Ser. II Dru\v stvo Mat. Fiz. Hrvatske}, VOLUME = {20}, YEAR = {1965}, PAGES = {51--55}, MRCLASS = {15.15}, MRNUMBER = {33 \#2657}, } @article {Dommanget63, AUTHOR = {Dommanget, J.}, TITLE = {L'inverse d'un cracovien rectangulaire: {S}on emploi dans la r\'esolution des syst\`emes d'\'equations lin\'eaires}, JOURNAL = {Publ. Sci. Tech. Minist\`ere de l'Air (Paris) Notes Tech. No.}, VOLUME = {128}, YEAR = {1963}, PAGES = {11--41}, MRCLASS = {15.15}, MRNUMBER = {31 \#3442}, } @article {DouglasPearcy63, AUTHOR = {Douglas, Jr., J. and Pearcy, C. M.}, TITLE = {On convergence of alternating direction procedures in the presence of singular operators}, JOURNAL = {Numer. Math.}, VOLUME = {5}, YEAR = {1963}, PAGES = {175--184}, MRCLASS = {65.65}, MRNUMBER = {27 \#4384}, } @article {DoustPrice64, AUTHOR = {Doust, A. and Price, V. E.}, TITLE = {The latent roots and vectors of a singular matrix}, JOURNAL = {Comput. J.}, VOLUME = {7}, YEAR = {1964}, PAGES = {222--227}, MRCLASS = {65.40}, MRNUMBER = {31 \#5322}, } @article {Dragomir65, AUTHOR = {Dragomir, A.}, TITLE = {On the generalized inverse of a matrix}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {3}, YEAR = {1965}, PAGES = {123--128}, MRCLASS = {15.15}, MRNUMBER = {37 \#5231}, } @inproceedings {DragomirADragomirP86, AUTHOR = {Dragomir, A. and Dragomir, P.}, TITLE = {Formulas of the {B}jerhammar type for the generalized inverse of an arbitrary matrix}, BOOKTITLE = {Proceedings of the {C}onference on {A}lgebra ({R}omanian) ({T}imi\c soara, 1986)}, PAGES = {33--36}, PUBLISHER = {Univ. Timi\c soara}, ADDRESS = {Timi\c soara}, YEAR = {1987}, MRCLASS = {15A09}, MRNUMBER = {90a:15002}, } @article {DragomirFildan69, AUTHOR = {Dragomir, A. and Fildan, M.}, TITLE = {L'inverse g\'en\'eralis\'e d'un op\'erateur lin\'eaire}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.}, VOLUME = {7}, YEAR = {1969}, PAGES = {55--65}, MRCLASS = {47.10}, MRNUMBER = {41 \#9020}, } @article {DragomirP63, AUTHOR = {Dragomir, P.}, TITLE = {On the {G}reville-{M}oore formula for calculating the generalized inverse matrix}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {1}, YEAR = {1963}, PAGES = {115--119}, MRCLASS = {15.15}, MRNUMBER = {30 \#2024}, } @article {DragomirP64, AUTHOR = {Dragomir, P.}, TITLE = {The generalized inverse of a bilinear form}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {2}, YEAR = {1964}, PAGES = {71--76}, MRCLASS = {15.70}, MRNUMBER = {32 \#1212}, } @ARTICLE{Drazin58, author = {Drazin, M. P.}, title = {Pseudo inverses in associative rings and semigroups}, journal = AMEMM, year = {1958}, volume = {65}, pages = {506--514}, keywords = {}, } @article {Drazin78, AUTHOR = {Drazin, M. P.}, TITLE = {Natural structures on semigroups with involution}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {84}, YEAR = {1978}, NUMBER = {1}, PAGES = {139--141}, MRCLASS = {20M10 (20M20)}, MRNUMBER = {58 \#6003}, } @inproceedings{Drazin82, AUTHOR = {Drazin, M. P.}, TITLE = {Differentiation of generalized inverses}, CROSSREF = {Campbell82a}, PAGES = {138--144}, YEAR = {1982}, MRCLASS = {15A09}, MRNUMBER = {83k:15005}, KEYWORDS = {matder, gen, invMP, algr}, } @article {Drazin86, AUTHOR = {Drazin, M. P.}, TITLE = {A partial order in completely regular semigroups}, JOURNAL = {J. Algebra}, VOLUME = {98}, YEAR = {1986}, PAGES = {362--374}, } @article{Drazin92, AUTHOR = {Drazin, M. P.}, TITLE = {Extremal definitions of generalized inverses}, JOURNAL = LINAA1, VOLUME = {165}, YEAR = {1992}, PAGES = {185--196}, } @article {Druilhet99, AUTHOR = {Druilhet, Pierre}, TITLE = {Optimality of neighbour balanced designs}, JOURNAL = {J. Statist. Plann. Inference}, FJOURNAL = {Journal of Statistical Planning and Inference}, VOLUME = {81}, YEAR = {1999}, NUMBER = {1}, PAGES = {142--152}, MRCLASS = {62K05 (62K10)}, MRNUMBER = {2000f:62174}, } @PHDTHESIS{Drygalla80, author = {Drygalla, V.}, title = {Zur {D}arstellung und {B}erechnung von verallgemeinerten inversen {M}atrizen}, school = {Martin-Luther Universit{\"a}t}, year = {1980}, type = {Mathematics Dissertation}, address = {Halle-Wirtenberg}, } @preamble{ "\def\cprime{$'$} " } @article {Drygalla82, AUTHOR = {Drygalla, V.}, TITLE = {Refinement of pseudosolutions of a system of linear equations}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u \i \ Matematiki i Matematichesko\u \i \ Fiziki}, VOLUME = {22}, YEAR = {1982}, NUMBER = {5}, PAGES = {1027--1032, 1275}, MRCLASS = {65F10 (15A09)}, MRNUMBER = {84a:65026}, NOTE = {(English translation: \textit{U.S.S.R. Comput. Math. and Math. Phys} \textbf{22}(1982), 1--7)}, } @article {Drygalla86, AUTHOR = {Drygalla, V.}, TITLE = {Zur {B}erechnung von {L}\"osungen konsistenter linearer {G}leichungssysteme mit singul\"arer {K}oeffizientenmatrix}, JOURNAL = {Computing}, FJOURNAL = {Computing. Archives for Scientific Computing}, VOLUME = {36}, YEAR = {1986}, NUMBER = {1-2}, PAGES = {163--168}, MRCLASS = {65F05 (65F10)}, MRNUMBER = {87d:65031}, } @article {Drygas69, AUTHOR = {Drygas, H.}, TITLE = {On a generalization of the {F}arkas theorem}, JOURNAL = {Unternehmensforschung}, VOLUME = {13}, YEAR = {1969}, PAGES = {283--290}, MRCLASS = {90.58}, MRNUMBER = {44 \#3701}, } @BOOK{Drygas70, author = {Drygas, H.}, title = {The {C}oordinate--{F}ree {A}pproach to {G}auss--{M}arkov {E}stimation}, publisher = {Springer--Verlag}, address = {Berlin}, year = {1970}, PAGES = {viii+113}, MRCLASS = {62.55}, MRNUMBER = {43 \#7016}, } @ARTICLE{Drygas71, author = {Drygas, H.}, title = {Consistency of the least squares and {G}auss--{M}arkov estimators in regression models}, journal = {Z. Wahrscheinlichkeitstheorie u. verw. Gebiete}, year = {1971}, volume = {17}, pages = {309--326}, keywords = {}, } @article {Drygas75, AUTHOR = {Drygas, H.}, TITLE = {Estimation and prediction for linear models in general spaces ({V}ortr\"age auf der {E}rsten {S}ommerschule \"uber {P}robleme der {M}odellwahl und {P}arametersch\"atzung in der {R}egressions-{A}nalyse, {Z}innowitz, 1974)}, JOURNAL = {Math. Operationsforsch. Statist.}, VOLUME = {6}, YEAR = {1975}, NUMBER = {2}, PAGES = {301--324}, MRCLASS = {62J05}, MRNUMBER = {58 \#31609}, KEYWORDS = {GauMar, his, spac, appst}, } @article {Drygas76, AUTHOR = {Drygas, H.}, TITLE = {Gauss-{M}arkov estimation for multivariate linear models with missing observations}, JOURNAL = {Ann. Statist.}, VOLUME = {4}, YEAR = {1976}, NUMBER = {4}, PAGES = {779--787}, MRCLASS = {62J05}, MRNUMBER = {53 \#14799}, } @article {Drygas85, AUTHOR = {Drygas, H.}, TITLE = {On the unified theory of least squares}, JOURNAL = {Probab. Math. Statist.}, FJOURNAL = {Probability and Mathematical Statistics}, VOLUME = {5}, YEAR = {1985}, NUMBER = {2}, PAGES = {177--186}, MRCLASS = {62J05}, MRNUMBER = {87j:62103}, } @article {DrygasSrzednicka76, AUTHOR = {Drygas, H. and Srzednicka, J.}, TITLE = {A new result on {H}su's model of regression analysis}, JOURNAL = {Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys.}, VOLUME = {24}, YEAR = {1976}, NUMBER = {12}, PAGES = {1133--1136}, MRCLASS = {62J05}, MRNUMBER = {55 \#9425}, } @inproceedings{Duffin71, author = {Duffin, R. J.}, crossref = {WilfHarary71}, title = {Network models}, year = {1971}, pages = {65--91}, } @article {DuffinMorley79, AUTHOR = {Duffin, R. J. and Morley, T. D.}, TITLE = {Inequalities induced by network connections. {I}{I}. {H}ybrid connections}, JOURNAL = JMATA, VOLUME = {67}, YEAR = {1979}, NUMBER = {1}, PAGES = {215--231}, MRCLASS = {94C05}, MRNUMBER = {84h:94020b}, KEYWORDS = {appnet, parsum}, } @inproceedings{DuffinMorley82, AUTHOR = {Duffin, R. J. and Morley, T. D.}, TITLE = {Inequalities induced by network connections}, CROSSREF = {Campbell82a}, PAGES = {27--49}, YEAR = {1982}, MRCLASS = {94C05}, KEYWORDS = {appnet, parsum}, MRNUMBER = {84h:94020a}, } @article {DuffinSchaeffer52, AUTHOR = {Duffin, R. J. and Schaeffer, A. C.}, TITLE = {A class of nonharmonic {F}ourier series}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {72}, YEAR = {1952}, PAGES = {341--366}, MRCLASS = {}, MRNUMBER = {13:839a}, KEYWORDS = {Frames}, } @article {DuffinTrapp72, AUTHOR = {Duffin, R. J. and Trapp, G. E.}, TITLE = {Hybrid addition of matrices-network theory concept}, JOURNAL = {Applicable Anal.}, VOLUME = {2}, YEAR = {1972/73}, PAGES = {241--254}, MRCLASS = {94A20}, MRNUMBER = {52 \#16873}, } @article {Duke70, AUTHOR = {Duke, J. W.}, TITLE = {A note on {EP} linear transformations}, JOURNAL = LINAA1, VOLUME = {3}, YEAR = {1970}, PAGES = {379--382}, MRCLASS = {15.05}, MRNUMBER = {42 \#1836}, } @article {DuncanHorn72, AUTHOR = {Duncan, D. B. and Horn, S. D.}, TITLE = {Linear dynamic recursive estimation from the viewpoint of regression analysis}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {67}, YEAR = {1972}, PAGES = {815--821}, MRCLASS = {62J05 (93E10)}, MRNUMBER = {50 \#11642}, NOTE = {(connection between Kalman filter and least-squares regression))}, } @BOOK{DunfordSchwartz57, author = {Dunford, N. and Schwartz, J. T.}, title = {Linear {O}perators. {P}art {I}}, publisher = {Interscience}, year = {1957}, address = {New York}, } @article {DunneStone93, AUTHOR = {Dunne, T. T. and Stone, M.}, TITLE = {Downdating the {M}oore-{P}enrose generalized inverse for cross-validation of centred least squares prediction}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {55}, YEAR = {1993}, NUMBER = {2}, PAGES = {369--375}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {94h:15002}, KEYWORDS = {appst, invMP}, } @article {DuPreKass92, AUTHOR = {DuPr{\'e}, Arthur M. and Kass, Seymour}, TITLE = {Distance and parallelism between flats in ${\R}^n$}, JOURNAL = LINAA1, VOLUME = {171}, YEAR = {1992}, PAGES = {99--107}, MRCLASS = {15A03 (15A06)}, MRNUMBER = {93f:15001}, } @article {Duris71, AUTHOR = {Duris, C. S.}, TITLE = {Optimal quadrature formulas using generalized inverses. {I}. {G}eneral theory and minimum variance formulas}, JOURNAL = {Math. Comp.}, VOLUME = {25}, YEAR = {1971}, PAGES = {495--504}, MRCLASS = {65D30}, MRNUMBER = {45 \#4633}, } @article {DurisSreedharan68, AUTHOR = {Duris, C. S. and Sreedharan, V. P.}, TITLE = {Chebyshev and $l\sp{1}$-solutions of linear equations using least squares solutions}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {5}, YEAR = {1968}, PAGES = {491--505}, MRCLASS = {65.35}, MRNUMBER = {38 \#4011}, } @article {Dwyer67, AUTHOR = {Dwyer, P. S.}, TITLE = {Some applications of matrix derivatives in multivariate analysis}, JOURNAL = {J. Amer. Statist. Assoc}, VOLUME = {62}, YEAR = {1967}, PAGES = {607--625}, MRCLASS = {62.40}, MRNUMBER = {35 \#7486}, } @article {DwyerMacphail48, AUTHOR = {Dwyer, P. S. and Macphail, M. S.}, TITLE = {Symbolic matrix derivatives}, JOURNAL = {Ann. Math. Statistics}, VOLUME = {19}, YEAR = {1948}, PAGES = {517--534}, MRCLASS = {09.0X}, MRNUMBER = {10,278h}, } @article {DzumaevMuhamadiev80, AUTHOR = {D{\v{z}}umaev, S. and Muhamadiev, {\`E}.}, TITLE = {Some properties of a pseudoinverse operator}, JOURNAL = {Dokl. Akad. Nauk Tadzhik. SSR}, FJOURNAL = {Doklady Akademii Nauk Tadzhiksko\u \i \ SSR}, VOLUME = {23}, YEAR = {1980}, NUMBER = {1}, PAGES = {3--5}, MRCLASS = {47A05}, MRNUMBER = {81f:47002}, } @article {Eagambaram88, AUTHOR = {Eagambaram, N.}, TITLE = {Generalized inverses with nonnegative principal minors}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {111}, YEAR = {1988}, PAGES = {293--312}, MRCLASS = {15A09}, MRNUMBER = {89j:15008}, } @article {Eagambaram91, AUTHOR = {Eagambaram, N.}, TITLE = {$(i,j,\cdots,k)$-inverses via bordered matrices}, JOURNAL = {Sankhy\=a Ser. A}, FJOURNAL = {Sankhy\=a (Statistics). The Indian Journal of Statistics. Series A}, VOLUME = {53}, YEAR = {1991}, NUMBER = {3}, PAGES = {298--308}, MRCLASS = {15A09 (15A18)}, MRNUMBER = {93i:15003}, KEYWORDS = {Bordered matrices}, } @book{Eaton83, AUTHOR = {Eaton, M. L.}, TITLE = {Multivariate {S}tatistics}, NOTE = {A vector space approach}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1983}, PAGES = {xvi+512}, ISBN = {0-471-02776-6}, MRCLASS = {62Hxx (62A05)}, MRNUMBER = {86i:62086}, } @article{EckartYoung36, author = {C. Eckart and G. Young}, year = {1936}, title = {The Approximation of One Matrix by Another of Lower Rank}, journal = {Psychometrika}, volume = {1}, pages = {211-218}, KEYWORDS = {appst, alglin, svd, his}, } @article{EckartYoung39, author = {C. Eckart and G. Young}, year = {1939}, title = {A Principal Axis Transformation for Non-{Hermitian} Matrices}, journal = BULAM1, volume = {45}, pages = {118-121}, KEYWORDS = {alglin, svd, geom}, } @article {Egervary53, AUTHOR = {Egerv{\'a}ry, E.}, TITLE = {On a property of the projector matrices and its application to the canonical representation of matrix functions}, JOURNAL = {Acta Sci. Math. Szeged}, VOLUME = {15}, YEAR = {1953}, PAGES = {1--6}, MRCLASS = {09.0X}, MRNUMBER = {15,191d}, } @article {EiermannEtAl88, AUTHOR = {Eiermann, M. and Marek, I. and Niethammer, W.}, TITLE = {On the solution of singular linear systems of algebraic equations by semi-iterative methods}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {53}, YEAR = {1988}, NUMBER = {3}, PAGES = {265--283}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {89h:65049}, } @article {EisenstatIpsen95, AUTHOR = {Eisenstat, S. C. and Ipsen, I. C. F.}, TITLE = {Relative perturbation techniques for singular value problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {32}, YEAR = {1995}, NUMBER = {6}, PAGES = {1972--1988}, MRCLASS = {65F30}, MRNUMBER = {96k:65033}, } @article {EisenstatIpsen98, AUTHOR = {Eisenstat, S. C. and Ipsen, I. C. F.}, TITLE = {Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {38}, YEAR = {1998}, NUMBER = {3}, PAGES = {502--509}, MRCLASS = {65F15}, MRNUMBER = {99j:65056}, } @article {EisinbergEtAl01, AUTHOR = {Eisinberg, A. and Pugliese, P. and Salerno, N.}, TITLE = {Vandermonde matrices on integer nodes: the rectangular case}, JOURNAL = {Numer. Math.}, VOLUME = {87}, YEAR = {2001}, NUMBER = {4}, PAGES = {663--674}, MRCLASS = {65F35}, MRNUMBER = {1 815 730}, } @article {EitelbergHanselmann78, AUTHOR = {Eitelberg, E. and Hanselmann, H.}, TITLE = {Comments on: ``{O}n system realization by matrix generalized inverses''\ ({I}nternat. {J}. {C}ontrol {\bf 26} (1977), no. 5, 745--751) by {V}. {L}ovass-{N}agy, {R}. {J}. {M}iller and {D}. {L}. {P}owers}, JOURNAL = {Internat. J. Control}, VOLUME = {27}, YEAR = {1978}, NUMBER = {4}, PAGES = {651--652}, MRCLASS = {93B15}, MRNUMBER = {57 \#9179}, NOTE = {(see \cite{Lovass-NagyEtAl77})}, } @article{Elden80, author = {Eld\'en, L.}, year = {1980}, title = {Perturbation Theory for the Least Squares Problem with Linear Equality Constraints}, journal = SIAJN, volume = {17}, pages = {338-350}, KEYWORDS = {alglin, lsq, pert}, } @article{Elden83, author = {Eld\'en. L.}, year = {1983}, title = {A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems}, journal = {BIT}, volume = {22}, pages = {487-502}, KEYWORDS = {alglin, comp, lsq, invo}, } @article {ElfvingG52, AUTHOR = {Elfving, G.}, TITLE = {Optimum allocation in linear regression theory}, JOURNAL = {Ann. Math. Statistics}, VOLUME = {23}, YEAR = {1952}, PAGES = {255--262}, MRCLASS = {62.0X}, MRNUMBER = {13,963h}, } @article {Elfving98, AUTHOR = {Elfving, T.}, TITLE = {A stationary iterative pseudoinverse algorithm}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {38}, YEAR = {1998}, NUMBER = {2}, PAGES = {275--282}, MRCLASS = {65F10 (65F50)}, MRNUMBER = {99d:65105}, } @article {ElGhaouiLebret97, AUTHOR = {El Ghaoui, L. and Lebret, H.}, TITLE = {Robust solutions to least-squares problems with uncertain data}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {18}, YEAR = {1997}, NUMBER = {4}, PAGES = {1035--1064}, MRCLASS = {65F20 (15A06)}, MRNUMBER = {99c:65075}, KEYWORDS = {Least-squares, semidefinite programming, ill-condition, regularization}, } @ARTICLE{Elliott28, author = {Elliott, W. W.}, title = {Generalized {G}reen's functions for compatible differential systems}, journal = {Amer. J. Math.}, year = {1928}, volume = {50}, pages = {243--258}, } @ARTICLE{Elliott29, author = {Elliott, W. W.}, title = {{G}reen's functions for differential systems containing a parameter}, journal = {Amer. J. Math.}, year = {1929}, volume = {51}, pages = {397--416}, } @article {ElsnerIkramov98, AUTHOR = {Elsner, L. and Ikramov, Kh. D.}, TITLE = {Normal matrices: an update}, JOURNAL = LINAA1, VOLUME = {285}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {291--303}, MRCLASS = {15A60}, MRNUMBER = {2000h:15036}, NOTE = {(see \cite{GroneEtAl87})}, } @article {Elster99, AUTHOR = {Elster, C.}, TITLE = {Recovering wavefronts from difference measurements in lateral shearing interferometry}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {110}, YEAR = {1999}, NUMBER = {1}, PAGES = {177--180}, MRCLASS = {39A70 (47B39 65N21 78A10)}, MRNUMBER = {2000m:39049}, } @article {EnglGroetsch88, AUTHOR = {Engl, H. W. and Groetsch, C. W.}, TITLE = {A higher order approximation technique for restricted linear least-squares problems}, JOURNAL = {Bull. Austral. Math. Soc.}, VOLUME = {37}, YEAR = {1988}, NUMBER = {1}, PAGES = {121--130}, MRCLASS = {65J10 (45L10 65R20)}, MRNUMBER = {89g:65074}, } @book {EnglEtAl96, AUTHOR = {Engl, H. W. and Hanke, M. and Neubauer, A.}, TITLE = {Regularization of {I}nverse {P}roblems}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1996}, PAGES = {viii+321}, MRCLASS = {}, MRNUMBER = {97k:65145}, } @article {EnglKress81, AUTHOR = {Engl, H. W. and Kress, R.}, TITLE = {A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problems}, JOURNAL = {Math. Methods Appl. Sci.}, FJOURNAL = {Mathematical Methods in the Applied Sciences}, VOLUME = {3}, YEAR = {1981}, NUMBER = {2}, PAGES = {249--274}, MRCLASS = {78A30 (45B05 47A55)}, MRNUMBER = {83j:78008}, } @article {EnglNashed81, AUTHOR = {Engl, H. W. and Nashed, M. Z.}, TITLE = {New extremal characterizations of generalized inverses of linear operators}, JOURNAL = JMATA, VOLUME = {82}, YEAR = {1981}, NUMBER = {2}, PAGES = {566--586}, MRCLASS = {47A05 (47A50)}, MRNUMBER = {83f:47001}, } @incollection {EnglNeubauer87, AUTHOR = {Engl, H. W. and Neubauer, A.}, TITLE = {On projection methods for solving linear ill-posed problems}, BOOKTITLE = {Model {O}ptimization in {E}xploration {G}eophysics ({B}erlin, 1986)}, PAGES = {73--92}, PUBLISHER = {Vieweg}, ADDRESS = {Braunschweig}, YEAR = {1987}, MRCLASS = {65J10 (47A50)}, MRNUMBER = {90g:65078}, } @article {Englefield66, AUTHOR = {Englefield, M. J.}, TITLE = {The commuting inverses of a square matrix}, JOURNAL = {Proc. Cambridge Philos. Soc.}, VOLUME = {62}, YEAR = {1966}, PAGES = {667--671}, MRCLASS = {15.15}, MRNUMBER = {33 \#5651}, } @article {Enskog30, AUTHOR = {Enskog, D.}, TITLE = {{\"U}ber die {A}ufl{\"o}sung einer singularel {I}ntegralgleichung}, JOURNAL = {Acta Math. Uppsala}, VOLUME = {54}, YEAR = {1930}, PAGES = {177--184}, MRCLASS = {}, MRNUMBER = {}, } @PHDTHESIS{Erdelsky69, author = {Erdelsky, P. J.}, title = {Projections in a Normed Linear Space and a Generalization of the Pseudo--Inverse}, school = {California Inst. Tech.}, year = {1969}, type = {Doctoral dissertation in Mathematics}, address = {Pasadena, CA}, keywords = {}, } @ARTICLE{Erdelyi66, author = {Erd{\'e}lyi, I.}, title = {On partial isometries in finite dimensional {E}uclidean spaces}, journal = SIAJA, year = {1966}, volume = {14}, pages = {453--467}, } @ARTICLE{Erdelyi66a, author = {Erd{\'e}lyi, I.}, title = {On the ``reversed order law'' related to the generalized inverse of matrix products}, journal = JASSC, year = {1966}, volume = {13}, pages = {439--443}, } @ARTICLE{Erdelyi67, author = {Erd{\'e}lyi, I.}, title = {The quasi--commuting inverse for a square matrix}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1967}, volume = {42}, pages = {626--633}, } @ARTICLE{Erdelyi67a, author = {Erd{\'e}lyi, I.}, title = {On the matrix equation ${A}x=\lambda {B}x$}, journal = JMATA, year = {1967}, volume = {17}, pages = {119--132}, } @ARTICLE{Erdelyi68, author = {Erd{\'e}lyi, I.}, title = {Partial isometries closed under multiplication on {H}ilbert spaces}, journal = JMATA, year = {1968}, volume = {22}, pages = {546--551}, keywords = {}, } @ARTICLE{Erdelyi68a, author = {Erd{\'e}lyi, I.}, title = {Normal partial isometries closed under multiplication on unitary spaces}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1968}, volume = {43}, pages = {186--190}, keywords = {}, } @ARTICLE{Erdelyi68b, author = {Erd{\'e}lyi, I.}, title = {Partial isometries defined by a spectral property on unitary spaces}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII}, year = {1968}, volume = {44}, pages = {741--747}, } @inproceedings{Erdelyi68c, AUTHOR = {Erd{\'e}lyi, I.}, TITLE = {Partial isometries and generalized inverses}, CROSSREF = {BoullionOdell68}, PAGES = {203--217}, YEAR = {1968}, } @ARTICLE{Erdelyi72, author = {Erd{\'e}lyi, I.}, title = {A generalized inverse for arbitrary operators between Hilbert spaces}, journal = PROCPS, year = {1972}, volume = {71}, pages = {43--50}, keywords = {}, } @inproceedings{Erdelyi82, AUTHOR = {Erd{\'e}lyi, I.}, TITLE = {Spectral decompositions for generalized inversions}, CROSSREF = {Campbell82a}, PAGES = {261--274}, YEAR = {1982}, MRCLASS = {47B40 (47A10)}, MRNUMBER = {84e:47044}, KEYWORDS = {linop, spacB}, } @article {ErdelyiBen-Israel72, AUTHOR = {Erd{\'e}lyi, I. and Ben-Israel, A.}, TITLE = {Extremal solutions of linear equations and generalized inversion between {H}ilbert spaces}, JOURNAL = JMATA, VOLUME = {39}, YEAR = {1972}, PAGES = {298--313}, MRCLASS = {47A50}, MRNUMBER = {46 \#9778}, KEYWORDS = {spacH, lineq, linop, invMP, sollsq, solmin}, } @article {ErdelyiMiller70, AUTHOR = {Erd{\'e}lyi, I. and Miller, F. R.}, TITLE = {Decomposition theorems for partial isometries}, JOURNAL = JMATA, VOLUME = {30}, YEAR = {1970}, PAGES = {665--679}, KEYWORDS = {}, } @preamble{ "\def\cprime{$'$} " } @article {Erokhin99, AUTHOR = {Erokhin, V. I.}, TITLE = {A generalization of the {S}herman-{M}orrison identity to the case of a rank-one modification of a pseudo-inverse matrix of full rank}, JOURNAL = {Zh. Vychisl. Mat. Mat. Fiz.}, FJOURNAL = {Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki. Rossi\u\i skaya Akademiya Nauk}, VOLUME = {39}, YEAR = {1999}, NUMBER = {8}, PAGES = {1280--1282}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {1 719 151}, } @article {EschenbachEtAl94, AUTHOR = {Eschenbach, C. A. and Hall, F. J. and Li, Zhongshan}, TITLE = {Sign pattern matrices and generalized inverses}, JOURNAL = LINAA1, VOLUME = {211}, YEAR = {1994}, PAGES = {53--66}, MRCLASS = {15A09 (15A21)}, MRNUMBER = {95i:15003}, } @article {EvansEtAl96, AUTHOR = {Evans, D. J. and Sun, Wenyu and de Sampaio, R. J. B. and Yuan, J. Y.}, TITLE = {The restricted generalized inverses corresponding to constrained quadratic system}, JOURNAL = {Int. J. Comput. Math.}, VOLUME = {62}, YEAR = {1996}, NUMBER = {3-4}, PAGES = {285--296}, MRCLASS = {65F20}, MRNUMBER = {98d:65050}, } @article {FanHoffman55, AUTHOR = {Fan, Ky and Hoffman, A. J.}, TITLE = {Some metric inequalities in the space of matrices}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {6}, YEAR = {1955}, PAGES = {111--116}, MRCLASS = {09.0X}, MRNUMBER = {16,784j}, } @article {Fantappie28, AUTHOR = {Fantappi\`{e}, L.}, TITLE = {Le calcul des matrices}, JOURNAL = {C. R. Acad. Sci. Paris}, VOLUME = {186}, YEAR = {1928}, PAGES = {619--621}, NOTE = {(see \cite{Rinehart55})}, } @article {Farebrother76, AUTHOR = {Farebrother, R. W.}, TITLE = {Further results on the mean square error of ridge regression}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {38}, YEAR = {1976}, NUMBER = {3}, PAGES = {248--250}, MRCLASS = {62J05}, MRNUMBER = {58 \#31610}, } @article {Farebrother78, AUTHOR = {Farebrother, R. W.}, TITLE = {An historical note on recursive residuals}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {40}, YEAR = {1978}, NUMBER = {3}, PAGES = {373--375}, MRCLASS = {62-03}, MRNUMBER = {80b:62004}, KEYWORDS = {History, linear model}, } @article {Farebrother85, AUTHOR = {Farebrother, R. W.}, TITLE = {Relations among set estimators: A bibliographical note}, JOURNAL = {Technometrics}, VOLUME = {27}, YEAR = {1985}, PAGES = {85--86}, KEYWORDS = {Least-squares, linear model}, } @article {Farebrother99, AUTHOR = {Farebrother, R. W.}, TITLE = {A class of statistical estimators related to principal components}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {121--126}, MRCLASS = {62H12 (62H25)}, MRNUMBER = {2000a:62126}, } @article {FeatherstoneKhatib97, AUTHOR = {Featherstone, R. and Khatib, O.}, TITLE = {Load independence of the dynamically consistent inverse of the Jacobian matrix. Source}, JOURNAL = {International Journal of Robotics Research}, VOLUME = {16}, YEAR = {1997}, PAGES = {168--170}, NOTE = {}, } @BOOK{Federer69, author = {Federer, H.}, title = {Geometric {M}easure {T}heory}, publisher = {Springer-Verlag}, year = {1969}, address = {New York}, } @article {FelippaEtAl98, AUTHOR = {Felippa, C. A. and Park, K. C. and Justino Filho, M. R.}, TITLE = {The construction of free-free flexibility matrices as generalized stiffness inverses}, JOURNAL = {Computers \& Structures}, VOLUME = {68}, YEAR = {1998}, PAGES = {411--418}, } @BOOK{Feller50, author = {Feller, W.}, title = {An {I}ntroduction to {P}robability {T}heory and {A}pplications, {V}olume 1}, publisher = {J. Wiley}, year = {1950}, address = {New York}, } @article {Fenyo79, AUTHOR = {Feny{\H{o}}, I. S.}, TITLE = {Eine {D}arstellung der verallgemeinerten {I}nversen eines linearen {O}perators}, JOURNAL = {Ber. Math.-Statist. Sekt. Forsch. Graz}, NUMBER = {117}, YEAR = {1979}, PAGES = {i+15}, MRCLASS = {}, MRNUMBER = {81b:47023}, } @article {Fenyo80, AUTHOR = {Feny{\H{o}}, I. S.}, TITLE = {A representation of the generalized inverse in {H}ilbert spaces}, JOURNAL = {Rend. Sem. Mat. Fis. Milano}, FJOURNAL = {Rendiconti del Seminario Matematico e Fisico di Milano}, VOLUME = {50}, YEAR = {1980}, PAGES = {23--29 (1982)}, MRCLASS = {47A05 (47A50)}, MRNUMBER = {83j:47002}, } @article {Fenyo84, AUTHOR = {Feny{\H{o}}, I. S.}, TITLE = {An extension of a theorem of {T}ikhonov}, JOURNAL = {Stochastica}, VOLUME = {8}, YEAR = {1984}, NUMBER = {3}, PAGES = {219--228}, MRCLASS = {}, MRNUMBER = {87b:47012}, } @article {FenyoPaparoni86, AUTHOR = {Feny{\H{o}}, I. S. and Paparoni, E.}, TITLE = {On an approximation of generalized inverses}, JOURNAL = {Publ. Math. Debrecen}, VOLUME = {33}, YEAR = {1986}, NUMBER = {3-4}, PAGES = {239--247}, MRCLASS = {}, MRNUMBER = {88b:47003}, } @article {FerranteVidoni99, AUTHOR = {Ferrante, M. and Vidoni, P.}, TITLE = {A {G}aussian-generalized inverse {G}aussian finite-dimensional filter}, JOURNAL = {Stochastic Process. Appl.}, FJOURNAL = {Stochastic Processes and their Applications}, VOLUME = {84}, YEAR = {1999}, NUMBER = {1}, PAGES = {165--176}, MRCLASS = {60G35}, MRNUMBER = {2000i:60041}, } @article {Fiedler95, AUTHOR = {Fiedler, M.}, TITLE = {Moore--{P}enrose involutions in the classes of {L}aplacians and simplices}, JOURNAL = LINMA, VOLUME = {39}, YEAR = {1995}, NUMBER = {1-2}, PAGES = {171--178}, MRCLASS = {15A09 (05C50)}, MRNUMBER = {97e:15002}, } @article {FiedlerMarkham90, AUTHOR = {Fiedler, M. and Markham, T. L.}, TITLE = {Some connections between the {D}razin inverse, ${P}$-matrices, and the closure of inverse ${M}$-matrices}, JOURNAL = LINAA1, VOLUME = {132}, YEAR = {1990}, PAGES = {163--172}, MRCLASS = {15A09}, MRNUMBER = {91d:15006}, } @article {FiedlerMarkham93, AUTHOR = {Fiedler, M. and Markham, T. L.}, TITLE = {A characterization of the {M}oore-{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {179}, YEAR = {1993}, PAGES = {129--133}, MRCLASS = {15A09}, MRNUMBER = {93m:15006}, } @article {FillFishkind99, AUTHOR = {Fill, J. A. and Fishkind, D. E.}, TITLE = {The {M}oore-{P}enrose generalized inverse for sums of matrices}, JOURNAL = SIAJM1, VOLUME = {21}, YEAR = {1999}, NUMBER = {2}, PAGES = {629--635 (electronic)}, MRCLASS = {15A09}, MRNUMBER = {1 742 814}, KEYWORDS = {invMP, matsum}, } @article {FilmoreWilliams71, AUTHOR = {Filmore, P. A. and Williams, J. P.}, TITLE = {On operator ranges}, JOURNAL = {Advances in Math.}, VOLUME = {7}, YEAR = {1971}, NUMBER = {}, PAGES = {254--281}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Intersection projection}, } @article {Finzel94, AUTHOR = {Finzel, M.}, TITLE = {Linear approximation in $l\sp \infty\sb n$}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {76}, YEAR = {1994}, NUMBER = {3}, PAGES = {326--350}, MRCLASS = {41A65 (41A50)}, MRNUMBER = {95c:41067}, } @incollection {Finzel95, AUTHOR = {Finzel, M.}, TITLE = {Pl\"ucker-{G}rassmann coordinates and elementary vectors}, BOOKTITLE = {Approximation {T}heory {VIII}, {V}ol.\ 1 ({C}ollege {S}tation, {TX}, 1995)}, PAGES = {207--214}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1995}, MRCLASS = {15A03 (41A15)}, MRNUMBER = {98h:15002}, } @article {Finzel00, AUTHOR = {Finzel, M.}, TITLE = {Metric projection and stratification of the {G}rassmannian}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {308}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {109--119}, MRCLASS = {15A75 (41A65)}, MRNUMBER = {2001d:15031}, } @ARTICLE{Fisher67, author = {Fisher, A. G.}, title = {On construction and properties of the generalized inverse}, journal = SIAJA, year = {1967}, volume = {15}, pages = {269--272}, keywords = {}, } @BOOK{Fleming77, author = {Fleming, W.}, title = {Functions of {S}everal {V}ariables (2nd edition)}, publisher = {Springer-Verlag}, year = {1977}, address = {New York}, } @article{Fletcher68, author = {Fletcher, R.}, year = {1968}, title = {Generalized Inverse Methods for the Best Least Squares Solution of Systems of Non-Linear Equations}, journal = COMPJ, volume = {10}, pages = {392--399}, KEYWORDS = {nlop, ginv, lsq, lsqnl}, } @article{Fletcher69, author = {Fletcher, R.}, year = {1969}, title = {A technique for orthogonalization}, journal = {J. Inst. Math. Appl.}, volume = {5}, pages = {162--166}, } @inbook{Fletcher70, author = {Fletcher, R.}, year = {1970}, title = {Generalized inverses for nonlinear equations and optimization}, crossref = {Rabinowitz70}, pages = {75--85}, } @article {Flores79, AUTHOR = {Flores de Chela, D.}, TITLE = {Generalized inverses on normed vector spaces}, JOURNAL = LINAA1, VOLUME = {26}, YEAR = {1979}, PAGES = {243--263}, MRCLASS = {15A09}, MRNUMBER = {80e:15003}, } @article {Flores82, AUTHOR = {Flores de Chela, D.}, TITLE = {Approximations in the $l\sb{\infty }$\ norm and the generalized inverse}, JOURNAL = LINAA1, VOLUME = {42}, YEAR = {1982}, PAGES = {3--21}, MRCLASS = {15A09 (15A60 41A50)}, MRNUMBER = {84f:15008}, } @article {Flores87, AUTHOR = {Flores de Chela, D.}, TITLE = {Generalized inverses under the $l\sb 1$-norm}, JOURNAL = LINAA1, VOLUME = {94}, YEAR = {1987}, PAGES = {237--261}, MRCLASS = {15A09}, MRNUMBER = {88i:15007}, } @article {FlorschHinderer00, AUTHOR = {Florsch, N. and Hinderer, J.}, TITLE = {Bayesian estimation of the free core nutation parameters from the analysis of precise tidal gravity data}, JOURNAL = {Physics of The Earth and Planetary Interiors}, VOLUME = {117}, YEAR = {2000}, PAGES = {21--35}, } @article {Forsgren96, AUTHOR = {Forsgren, A.}, TITLE = {On linear least-squares problems with diagonally dominant weight matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {17}, YEAR = {1996}, NUMBER = {4}, PAGES = {763--788}, MRCLASS = {65F20 (65F35 65K05)}, MRNUMBER = {97g:65084}, } @Article{ForsgrenSporre01, author = {Forsgren, A. and Sporre, G.}, title = {On weighted linear least-squares problems related to interior methods for convex quadratic programming}, journal = {SIAM J. Matrix Anal. Appl.}, year = 2001, volume = {23}, pages = {42--56}, } @ARTICLE{Forsythe70, author = {Forsythe, G. E.}, title = {The maximum and minimum of a positive definite quadratic polynomial on a sphere are convex functions of the radius}, journal = SIAJA, year = {1970}, volume = {19}, pages = {551--554}, keywords = {}, } @ARTICLE{ForsytheGolub65, author = {Forsythe, G. E. and Golub, G. H.}, title = {On the stationary values of a second--degree polynomial on the unit sphere}, journal = SIAJA, year = {1965}, volume = {13}, pages = {1050--1068}, } @article {Foster61, AUTHOR = {Foster, M.}, TITLE = {An application of the {W}iener-{K}olmogorov smoothing theory to matrix inversion}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {9}, YEAR = {1961}, PAGES = {387--392}, MRCLASS = {65.35}, MRNUMBER = {26 \#3178}, } @article {Foulis60, AUTHOR = {Foulis, D. J.}, TITLE = {Baer $\sp{\ast} $-semigroups}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {11}, YEAR = {1960}, PAGES = {648--654}, MRCLASS = {06.40}, MRNUMBER = {23 \#A3105}, } @ARTICLE{Foulis63, author = {Foulis, D. J.}, title = {Relative inverses in {B}aer${}^*$--semigroups}, journal = {Michigan Math. J.}, year = {1963}, volume = {10}, pages = {65--84}, } @ARTICLE{Frame64, author = {Frame, J. S.}, title = {Matrix functions and applications. {I}. Matrix operations and generalized inverses}, journal = {IEEE Spectrum}, year = {1964}, volume = {1}, pages = {209--220}, } @article {Frame64a, AUTHOR = {Frame, J. S.}, TITLE = {Matrix functions and applications. {II}. {F}unctions of a matrix}, JOURNAL = {IEEE Spectrum}, VOLUME = {1}, YEAR = {1964}, NUMBER = {4}, PAGES = {102--108}, MRCLASS = {15.25 (15.30)}, MRNUMBER = {32 \#1196}, } @article {Frame64b, AUTHOR = {Frame, J. S.}, TITLE = {Matrix functions and applications. {IV}. {M}atrix functions and constituent matrices}, JOURNAL = {IEEE Spectrum}, VOLUME = {1}, YEAR = {1964}, NUMBER = {6}, PAGES = {123--131}, MRCLASS = {15.30}, MRNUMBER = {32 \#1198}, } @article {Frame64c, AUTHOR = {Frame, J. S.}, TITLE = {Matrix functions and applications. {V}. {S}imilarity reductions by rational or orthogonal matrices}, JOURNAL = {IEEE Spectrum}, VOLUME = {1}, YEAR = {1964}, NUMBER = {7}, PAGES = {103--109}, MRCLASS = {15.30}, MRNUMBER = {32 \#1199}, } @article {FrameKoenig64, AUTHOR = {Frame, J. S. and Koenig, H. E.}, TITLE = {Matrix functions and applications. {III}. {A}pplications of matrices to systems analysis}, JOURNAL = {IEEE Spectrum}, VOLUME = {1}, YEAR = {1964}, NUMBER = {5}, PAGES = {100--109}, MRCLASS = {15.99 (93.99)}, MRNUMBER = {32 \#1197}, } @article {FranchettiCheney78, AUTHOR = {Franchetti, C. and Cheney, E. W.}, TITLE = {Orthogonal projections in spaces of continuous functions}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {63}, YEAR = {1978}, NUMBER = {1}, PAGES = {253--264}, MRCLASS = {41A65}, MRNUMBER = {58 \#1923}, } @incollection {Franck62, AUTHOR = {Franck, P.}, TITLE = {Sur la distance minimale d'une matrice r{\'e}guli{\`e}re donn{\'e}e au lieu des matrices singuli{\`e}res}, BOOKTITLE = {Deux. {C}ongr. {A}ssoc. {F}ranc. {C}alcul. et {T}rait. {I}nform. {P}aris 1961}, PAGES = {55--60}, PUBLISHER = {Gauthiers--Villars}, ADDRESS = {Paris}, YEAR = {1962}, MRNUMBER = {29 \#2953}, } @ARTICLE{Fredholm03, author = {Fredholm, I.}, title = {Sur une classe d'\'equations fonctionnelles}, journal = {Acta Math.}, year = {1903}, volume = {27}, pages = {365--390}, } @incollection {FriedlanderEtAl78, AUTHOR = {Friedlander, A. and Mart{\'\i}nez, J. M. and Scolnik, H. D.}, TITLE = {Generalized inverses and a new stable secant type minimization algorithm}, BOOKTITLE = {Optimization {T}echniques ({P}roc. 8th {IFIP} {C}onf., {W}{\"u}rzburg, 1977), {P}art 2}, PAGES = {136--146. Lecture Notes in Control and Informat. Sci., Vol. 7}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1978}, MRCLASS = {65K05 (90C30)}, MRNUMBER = {58 \#13708}, KEYWORDS = {Nonlinear equations}, } @article {FujiiEtAl00, AUTHOR = {Fujii, Masatoshi and Furuta, Takayuki and Nakamoto, Ritsuo}, TITLE = {Applications of {G}ramian transformation formula}, JOURNAL = {Sci. Math.}, FJOURNAL = {Scientiae Mathematicae}, VOLUME = {3}, YEAR = {2000}, NUMBER = {1}, PAGES = {81--86 (electronic)}, MRCLASS = {47A05 (15A15)}, MRNUMBER = {2001c:47002}, } @article {Fulton78, AUTHOR = {Fulton, J. D.}, TITLE = {Generalized inverses of matrices over a finite field}, JOURNAL = {Discrete Math.}, VOLUME = {21}, YEAR = {1978}, NUMBER = {1}, PAGES = {23--29}, MRCLASS = {15A09}, MRNUMBER = {80c:15002}, } @article {Fulton79, AUTHOR = {Fulton, J. D.}, TITLE = {Generalized inverses of matrices over fields of characteristic two}, JOURNAL = LINAA1, VOLUME = {28}, YEAR = {1979}, PAGES = {69--76}, MRCLASS = {15A09 (15A23 15A33)}, MRNUMBER = {80i:15004}, } @article {FunderlicMeyer86, AUTHOR = {Funderlic, R. E. and Meyer, Jr., C. D.}, TITLE = {Sensitivity of the stationary distribution vector for an ergodic {M}arkov chain}, JOURNAL = LINAA1, VOLUME = {76}, YEAR = {1986}, PAGES = {1--17}, MRCLASS = {60J10 (65F35)}, MRNUMBER = {87f:60102}, KEYWORDS = {appmar, pert}, } @ARTICLE{Gabriel65, author = {Gabriel, R.}, title = {Extensions of generalized algebraic complement to arbitrary matrices (Romanian)}, journal = {Stud. Cerc. Mat.}, year = {1965}, volume = {17}, pages = {1567--1581}, MRNUMBER = {35 \#6703}, } @ARTICLE{Gabriel69, author = {Gabriel, R.}, title = {Das verallgemeinerte {I}nverse einer {M}atrix deren {E}lemente {\"u}ber einem beliebigen {K}{\"o}rper angeh{\"o}ren}, journal = {J. Reine Angew. Math.}, year = {1969}, volume = {234}, pages = {107--122}, MRNUMBER = {41 \#1753}, } @ARTICLE{Gabriel70, author = {Gabriel, R.}, title = {Das verallgemeinerte {I}nverse einer {M}atrix {\"u}ber einem beliebigen {K}{\"o}rperanalytisch betrachtet}, journal = {J. Reine Angew. Math.}, year = {1970}, volume = {244}, pages = {83--93}, } @article {Gabriel75, AUTHOR = {Gabriel, R.}, TITLE = {Das verallgemeinerte {I}nverse einer {M}atrix \"uber einen beliebigen {K}\"orper---mit {S}kelettzerlegungen berechnet}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, VOLUME = {20}, YEAR = {1975}, PAGES = {213--225}, MRCLASS = {15A09}, MRNUMBER = {52 \#8141}, } @article {Gabriel75a, AUTHOR = {Gabriel, R.}, TITLE = {Das verallgemeinerte {I}nverse in {A}lgebren}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, VOLUME = {20}, YEAR = {1975}, PAGES = {311--324}, MRCLASS = {15A09 (16A28)}, MRNUMBER = {52 \#8143}, NOTE = {(corrigendum: Rev. Roumaine Math. Pures Appl. \textbf{20}(1975), 747)}, } @article {GabrielHartwig84, AUTHOR = {Gabriel, R. and Hartwig, R. E.}, TITLE = {The {D}razin inverse as a gradient}, JOURNAL = LINAA1, VOLUME = {63}, YEAR = {1984}, PAGES = {237--252}, MRCLASS = {15A09}, MRNUMBER = {85k:15004}, KEYWORDS = {invD, matder}, } @article {GachesEtAl65, AUTHOR = {Gaches, J. and Rigal, {J.-L.} and Rousset de Pina, X.}, TITLE = {Distance euclidienne d'une application lin{\'e}aire $\sigma$ au lieu des applications de rang $r$ donn{\'e}}, JOURNAL = {C. R. Acad. Sci. Paris}, VOLUME = {260}, YEAR = {1965}, PAGES = {5672--5674}, } @article {Galantai00, AUTHOR = {Gal{\'a}ntai, A.}, TITLE = {The theory of {N}ewton's method}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {124}, YEAR = {2000}, NUMBER = {1-2}, PAGES = {25--44}, MRCLASS = {65J15 (47J25 65-02)}, MRNUMBER = {1 803 292}, NOTE = {(Numerical analysis 2000, Vol. IV, Optimization and nonlinear equations)}, } @article {GalantaiVarga76, AUTHOR = {Gal{\'a}ntai, A. and Varga, G.}, TITLE = {A relaxation method for the computation of generalized inverses of matrices}, JOURNAL = {K\"ozlem\'enyek---MTA Sz\'amit\'astechn. Automat. Kutato Int. Budapest}, NUMBER = {17}, YEAR = {1976}, PAGES = {57--62}, MRCLASS = {65F20}, MRNUMBER = {57 \#4497}, } @preamble{ "\def\cprime{$'$} " } @article {Galba94, AUTHOR = {Galba, E. F.}, TITLE = {Weighted pseudo-inversion of matrices with singular weights}, JOURNAL = {Ukra\"\i n. Mat. Zh.}, FJOURNAL = {Akadem\=\i ya Nauk Ukra\"\i ni. \=Institut Matematiki. Ukra\"\i ns\cprime ki\u\i\ Matematichni\u\i\ Zhurnal}, VOLUME = {46}, YEAR = {1994}, NUMBER = {10}, PAGES = {1323--1327}, MRCLASS = {15A09}, MRNUMBER = {96h:15002}, } @preamble{ "\def\cprime{$'$} " } @article {Galba96, AUTHOR = {Galba, E. F.}, TITLE = {Iterative methods for computing a weighted pseudo-inverse matrix}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {36}, YEAR = {1996}, NUMBER = {6}, PAGES = {28--39}, ISSN = {0044-4669}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {97h:65041}, } @preamble{ "\def\cprime{$'$} " } @article {Galba97, AUTHOR = {Galba, E. F.}, TITLE = {Representation of a weighted pseudo-inverse matrix in terms of other pseudo-inverse matrices}, JOURNAL = {Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki}, FJOURNAL = {Dopov\=\i d\=\i\ Nats\=\i onal\cprime no\"\i\ Akadem\=\i \"\i\ Nauk Ukra\"\i ni. Matematika. Prirodoznavstvo. Tekhn\=\i chn\=\i\ Nauki}, YEAR = {1997}, NUMBER = {4}, PAGES = {12--17}, MRCLASS = {15A09}, MRNUMBER = {99b:15001}, } @preamble{ "\def\cprime{$'$} " } @article {GalbaEtAl99, AUTHOR = {Galba, E. F. and Molchanov, I. N. and Skopetski{\u\i}, V. V.}, TITLE = {Iterative methods for computing a weighted pseudo-inverse matrix with singular weights}, JOURNAL = {Kibernet. Sistem. Anal.}, FJOURNAL = {Natsional\cprime naya Akademiya Nauk Ukrainy. Institut Kibernetiki im. V. M. Glushkova. Kibernetika i Sistemny\u\i\ Analiz}, YEAR = {1999}, NUMBER = {5}, PAGES = {150--169, 191}, MRCLASS = {65F20}, MRNUMBER = {2001b:65047}, } @article{GallantGerig80, AUTHOR = {Gallant, A. R. and Gerig, T. M.}, TITLE = {Computations for constrained linear models}, JOURNAL = {J. Econometrics}, FJOURNAL = {Journal of Econometrics}, VOLUME = {12}, YEAR = {1980}, NUMBER = {1}, PAGES = {59--84}, MRCLASS = {62J05}, MRNUMBER = {81m:62123}, KEYWORDS = {maximum likelihood estimation, Moore-Penrose}, NOTE = {(see \cite{Corradi82})}, } @article {GalperinWaksman80, AUTHOR = {Galperin, A. M. and Waksman, Z.}, TITLE = {On pseudo-inverses of operator products}, JOURNAL = LINAA1, VOLUME = {33}, YEAR = {1980}, PAGES = {123--131}, MRCLASS = {15A09 (47A05)}, MRNUMBER = {82f:15003}, } @article {GalperinWaksman98, AUTHOR = {Galperin, A. M. and Waksman, Z.}, TITLE = {Ulm's method under regular smoothness}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = {Numerical Functional Analysis and Optimization. An International Journal}, VOLUME = {19}, YEAR = {1998}, NUMBER = {3-4}, PAGES = {285--307}, MRCLASS = {65J15 (47J25)}, MRNUMBER = {2000k:65105}, } @article {Gander90, AUTHOR = {Gander, W.}, TITLE = {Algorithms for the polar decomposition}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, VOLUME = {11}, YEAR = {1990}, NUMBER = {6}, PAGES = {1102--1115}, MRCLASS = {65F30}, MRNUMBER = {91j:65070}, } @BOOK{Gantmacher59, author = {Gantmacher, F. R.}, title = {The {T}heory of {M}atrices}, publisher = {Chelsea}, year = {1959}, volume = {I and {II}}, address = {New York}, } @article {GaoAntsaklis91, AUTHOR = {Gao, Zhiqiang and Antsaklis, P. J.}, TITLE = {Stability of the pseudo-inverse method for reconfigurable control systems}, JOURNAL = {Internat. J. Control}, FJOURNAL = {International Journal of Control}, VOLUME = {53}, YEAR = {1991}, NUMBER = {3}, PAGES = {717--729}, MRCLASS = {93B40}, MRNUMBER = {91m:93056}, } @article {GarnettEtAl71, AUTHOR = {Garnett III, J. M. and Ben-Israel, A. and Yau, S. S.}, TITLE = {A hyperpower iterative method for computing matrix products involving the generalized inverse}, JOURNAL = SIAJN, VOLUME = {8}, YEAR = {1971}, PAGES = {104--109}, } @article {GavurinFarforovskaja66, AUTHOR = {Gavurin, M. K. and Farforovskaja, Ju. B.}, TITLE = {An iterative method for finding the minimum of sums of squares}, JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {6}, YEAR = {1966}, PAGES = {1094--1097}, MRCLASS = {65.30}, MRNUMBER = {34 \#2159}, } @article {Gay77, AUTHOR = {Gay, D. M.}, TITLE = {Modifying singular values: existence of solutions to sytems of nonlinear equations having a possibly singular {J}acobian matrix}, JOURNAL = {Math. Comp.}, VOLUME = {31}, YEAR = {1977}, NUMBER = {140}, PAGES = {962--973}, MRCLASS = {65H10}, MRNUMBER = {56 \#1695}, } @article {Gay79, AUTHOR = {Gay, D. M.}, TITLE = {Corrigenda: ``{M}odifying singular values: existence of solutions to systems of nonlinear equations having a possibly singular {J}acobian matrix''\ ({M}ath. {C}omp. {\bf 31}(1977), no. 140, 962--973)}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {33}, YEAR = {1979}, NUMBER = {145}, PAGES = {432--433}, MRCLASS = {65H10}, MRNUMBER = {80g:65055}, } @article {GeorgeIkramov96, AUTHOR = {George, A. and Ikramov, Kh. D.}, TITLE = {Is the polar decomposition finitely computable?}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {17}, YEAR = {1996}, NUMBER = {2}, PAGES = {348--354}, MRCLASS = {15A23 (15A18 65F10)}, MRNUMBER = {96m:15023}, KEYWORDS = {Polar decomposition}, NOTE = {(see \cite{GeorgeIkramov97})}, } @article {GeorgeIkramov97, AUTHOR = {George, A. and Ikramov, Kh. D.}, TITLE = {Addendum: ``{I}s the polar decomposition finitely computable?'' [{S}{I}{A}{M} {J}. {M}atrix {A}nal.\ {A}ppl.\ {\bf 17} (1996), no.\ 2, 348--354; {M}{R} 96m:15023]}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {18}, YEAR = {1997}, NUMBER = {1}, PAGES = {264}, MRCLASS = {15A23 (15A18 65F10)}, MRNUMBER = {97m:15022}, } @article {GerigGallant75, AUTHOR = {Gerig, T. M. and Gallant, A. R.}, TITLE = {Computing methods for linear models subject to linear parametric constraints}, JOURNAL = {J. Statist. Comput. Simulation}, VOLUME = {3}, YEAR = {1975}, PAGES = {283--296}, MRCLASS = {62J05 (65F30)}, MRNUMBER = {52 \#4534}, KEYWORDS = {Constrained least squares}, NOTE = {(Errata: ibid 4 (1975), no. 1, 81--82)}, } @article {Germain-Bonne69, AUTHOR = {Germain--Bonne, B.}, TITLE = {Calcul de pseuodo--inverses}, JOURNAL = {Rev. Francaise Informat. Recherce Op{\'e}rationelle}, VOLUME = {3}, YEAR = {1969}, PAGES = {3--14}, } @book {GetsonHsuan88, AUTHOR = {Getson, A. J. and Hsuan, F. C.}, TITLE = {$\{2\}$-{I}nverses and their {S}tatistical {A}pplication}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1988}, PAGES = {x+110}, ISBN = {0-387-96849-0}, MRCLASS = {15A09 (62H15 62J05)}, MRNUMBER = {90e:15004}, } @article {GilsteinLeamer83, AUTHOR = {Gilstein, C. Z. and Leamer, E. E.}, TITLE = {The set of weighted regression estimates}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {78}, YEAR = {1983}, NUMBER = {384}, PAGES = {942--948}, MRCLASS = {62J05}, MRNUMBER = {85g:62113}, } @article {GiurescuGabriel64, AUTHOR = {Giurescu, C. and Gabriel, R.}, TITLE = {Some properties of the generalized matrix inverse and semiinverse}, JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.}, VOLUME = {2}, YEAR = {1964}, PAGES = {103--111}, MRCLASS = {15.15}, MRNUMBER = {32 \#118}, } @BOOK{GlazmanLjubich69, author = {Glazman, I. M. and Ljubich, Ju. I.}, title = {Finite {D}imensional {L}inear {A}nalysis}, publisher = {Nauka}, year = {1969}, address = {Moscow}, note = {(English translation published by MIT Press)}, } @BOOK{Goldberg66, author = {Goldberg, S.}, title = {Unbounded {L}inear {O}perators}, publisher = {McGraw-Hill Book Co.}, year = {1966}, address = {New York}, } @article {GoldmanZelen64, AUTHOR = {Goldman, A. J. and Zelen, M.}, TITLE = {Weak generalized inverses and minimum variance linear unbiased estimation}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {68B}, YEAR = {1964}, PAGES = {151--172}, MRCLASS = {62.55}, MRNUMBER = {30 \#3525}, } @BOOK{Goldstein67, author = {Goldstein, A. A.}, title = {Constructive {R}eal {A}nalysis}, publisher = {Harper and Row}, year = {1967}, address = {New York}, } @article {GoldsteinGoldstein00, AUTHOR = {Goldstein, G. R. and Goldstein, J. A.}, TITLE = {The best generalized inverse}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {252}, YEAR = {2000}, NUMBER = {1}, PAGES = {91--101}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {1 797 846}, } @article {GoldsteinM74, AUTHOR = {Goldstein, M. J.}, TITLE = {Reduction of the pseudoinverse of a {H}ermitian persymmetric matrix}, JOURNAL = {Math. Comp.}, VOLUME = {28}, YEAR = {1974}, PAGES = {715--717}, MRCLASS = {65F20}, MRNUMBER = {51 \#7268}, } @article {GoldsteinSmith74, AUTHOR = {Goldstein, M. and Smith, A. F. M.}, TITLE = {Ridge-type estimators for regression analysis}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {36}, YEAR = {1974}, PAGES = {284--291}, MRCLASS = {}, MRNUMBER = {54 \#6383}, } @article {Goller86, AUTHOR = {Goller, H.}, TITLE = {Shorted operators and rank decomposition matrices}, JOURNAL = LINAA1, VOLUME = {81}, YEAR = {1986}, PAGES = {207--236}, MRCLASS = {15A99}, MRNUMBER = {87k:15038}, } @ARTICLE{Golub65, author = {Golub, G. H.}, title = {Numerical methods for solving linear least squares problems}, journal = NUMEM, year = {1965}, volume = {7}, pages = {206--216}, } @ARTICLE{Golub68, author = {Golub, G. H.}, title = {Least squares, singular values and matrix approximations}, journal = {Aplikace Mathematiky}, year = {1968}, volume = {13}, pages = {44--51}, } @TECHREPORT{Golub69, author = {Golub, G. H.}, title = {Matrix decompositions and statistical calculations}, institution = {Stanford University}, year = {1969}, type = {Tech. Report}, number = {STAN-CS-124}, address = {Stanford}, month = {March}, } @article{GolubEtAl79, author = {Golub, G. H. and Heath, M. T. and Wahba, G.}, year = {1979}, title = {Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter}, journal = {Technometrics}, volume = {21}, pages = {215--223}, } @article {GolubEtAl87, AUTHOR = {Golub, G. H. and Hoffman, A. J. and Stewart, G. W.}, TITLE = {A generalization of the {E}ckart-{Y}oung-{M}irsky matrix approximation theorem}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {88/89}, YEAR = {1987}, PAGES = {317--327}, MRCLASS = {41A45 (15A60 62J05 65F99)}, MRNUMBER = {88f:41039}, } @article {GolubKahan65, AUTHOR = {Golub, G. H. and Kahan, W.}, TITLE = {Calculating the singular values and pseudo-inverse of a matrix}, JOURNAL = {J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.}, VOLUME = {2}, YEAR = {1965}, PAGES = {205--224}, MRCLASS = {65.35}, MRNUMBER = {32 \#587}, NOTE = {(see \cite{DeMeersman70})}, } @article {GolubMeyer86, AUTHOR = {Golub, G. H. and Meyer, Jr., C. D.}, TITLE = {Using the ${Q}{R}$ factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for {M}arkov chains}, JOURNAL = SIAJA1, VOLUME = {7}, YEAR = {1986}, NUMBER = {2}, PAGES = {273--281}, MRCLASS = {60J10 (65F05)}, MRNUMBER = {87i:60073}, KEYWORDS = {appmar, approb}, } @article{GolubPereyra73, author = {Golub, G. H. and Pereyra, V.}, year = {1973}, title = {The Differentiation of Pseudoinverses and Nonlinear Least Squares Problems Whose Variables Separate}, journal = SIAJN, volume = {10}, pages = {413--432}, KEYWORDS = {nlp, lsqnl, pert, mp, proj, lsq, matder}, } @inproceedings{GolubPereyra76, author = {Golub, G. H. and Pereyra, V.}, year = {1976}, title = {Differentiation of Pseudoinverses, Separable Nonlinear Least Squares Problems and Other Tales}, crossref = {Nashed76}, pages = {303--324}, KEYWORDS = {nlp, lsqnl, pert, mp, proj, lsq, matder}, } @article{GolubReinsch70, author = {Golub, G. H. and Reinsch, C.}, year = {1970}, title = {Singular value decompositions and least squares solutions}, journal = NUMEM, volume = {14}, pages = {403--420}, NOTE = {(republished, pp. 134--151 in \cite{WilkinsonReinsch71})}, KEYWORDS = {}, } @article{GolubStyan73, author = {Golub, G. H. and Styan, G. P. H.}, title = {Numerical computations for univariate linear models}, journal = {Journal of Statistical Computations and Simulation}, year = {1973}, volume = {2}, pages = {253--274}, } @book {GolubVanLoan96, AUTHOR = {Golub, G. H. and Van Loan, C. F.}, TITLE = {Matrix {C}omputations}, EDITION = {Third}, PUBLISHER = {Johns Hopkins University Press}, ADDRESS = {Baltimore, MD}, YEAR = {1996}, PAGES = {xxx+698}, ISBN = {0-8018-5413-X; 0-8018-5414-8}, MRCLASS = {65-02 (65Fxx)}, MRNUMBER = {97g:65006}, } @article{GolubWilkinson66, author = {G. H. Golub and J. H. Wilkinson}, year = {1966}, title = {Note on the iterative refinement of least squares solutions}, journal = NUMEM, volume = {9}, pages = {139--148}, } @article {GomezRomeu01, AUTHOR = {G{\'o}mez, A. and Romeu, D.}, TITLE = {A pseudoinverse for {F}rank's formula}, JOURNAL = {Acta Cryst. Sect. A}, FJOURNAL = {Acta Crystallographica. Section A: Foundations of Crystallography}, VOLUME = {57}, YEAR = {2001}, NUMBER = {1}, PAGES = {116--117}, MRCLASS = {82D25}, MRNUMBER = {1 805 576}, } @article {GongXEtAL98, AUTHOR = {Gong, Xiangyang and Chen, Wanyi and Tu, Fengsheng}, TITLE = {The stability and design of nonlinear neural networks}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {35}, YEAR = {1998}, NUMBER = {8}, PAGES = {1--7}, MRCLASS = {92B20}, MRNUMBER = {99b:92003}, } @article {GonzagaLara97, AUTHOR = {Gonzaga, C. C. and Lara, H. J.}, TITLE = {A note on properties of condition numbers}, JOURNAL = LINAA1, VOLUME = {261}, YEAR = {1997}, PAGES = {269--273}, MRCLASS = {15A12}, MRNUMBER = {98c:15020}, NOTE = {(see \cite{Ikramov99})}, } @ARTICLE{Good69, author = {Good, I. J.}, title = {Some applications of the singular decomposition of a matrix}, journal = {Technometrics}, year = {1969}, volume = {11}, pages = {823--831}, } @article {Good80, AUTHOR = {Good, I. J.}, TITLE = {Generalized determinants and generalized generalized variance}, JOURNAL = {J. Statist. Comput. Simulation}, VOLUME = {12}, YEAR = {1980/81}, NUMBER = {3-4}, PAGES = {311--315}, MRCLASS = {15A15 (15A18 62E99)}, MRNUMBER = {84c:15007}, NOTE = {(see \cite{Ben-Israel92})}, } @article {Gouveia93, AUTHOR = {Gouveia, M. C.}, TITLE = {Generalized invertibility of {H}ankel and {T}oeplitz matrices}, JOURNAL = LINAA1, VOLUME = {193}, YEAR = {1993}, PAGES = {95--106}, MRCLASS = {15A09 (15A57)}, MRNUMBER = {94j:15003}, } @article {Gouveia94, AUTHOR = {Gouveia, M. C.}, TITLE = {Group and {M}oore-{P}enrose invertibility of {B}ezoutians}, JOURNAL = LINAA1, VOLUME = {197/198}, YEAR = {1994}, PAGES = {495--509}, MRCLASS = {15A09 (15A15)}, MRNUMBER = {95g:15003}, } @ARTICLE{GouveiaPuystjens91, AUTHOR = {Gouveia, M. C. and Puystjens, R.}, TITLE = {About the group inverse and {M}oore-{P}enrose inverse of a product}, JOURNAL = LINAA1, VOLUME = {150}, YEAR = {1991}, PAGES = {361--369}, MRCLASS = {15A09}, MRNUMBER = {92b:15007}, } @article {MR86j:47065, AUTHOR = {Gramsch, B.}, TITLE = {Relative {I}nversion in der {S}t\"orungstheorie von {O}peratoren und $\Psi $-{A}lgebren}, JOURNAL = {Math. Ann.}, VOLUME = {269}, YEAR = {1984}, NUMBER = {1}, PAGES = {27--71}, MRCLASS = {47D99 (47A55 47G05 58B25 58G15)}, MRNUMBER = {86j:47065}, } @article {Graves-MorrisEtAl00, AUTHOR = {Graves--Morris, P. R. and Roberts, D. E. and Salam, A.}, TITLE = {The epsilon algorithm and related topics}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {122}, YEAR = {2000}, NUMBER = {1-2}, PAGES = {51--80}, MRCLASS = {65B05 (41A21)}, MRNUMBER = {1 794 652}, } @book {Graybill61, AUTHOR = {Graybill, F. A.}, TITLE = {An {I}ntroduction to {L}inear {S}tatistical {M}odels. {V}ol {I}}, PUBLISHER = {McGraw-Hill Book Co.}, ADDRESS = {Inc., New York}, YEAR = {1961}, PAGES = {xiii+463}, MRCLASS = {62.55}, MRNUMBER = {23 \#A3612}, } @book {Graybill76, AUTHOR = {Graybill, F. A.}, TITLE = {Theory and {A}pplication of the {L}inear {M}odel}, PUBLISHER = {Duxbury Press}, ADDRESS = {North Scituate, Mass.}, YEAR = {1976}, PAGES = {xiv+704}, MRCLASS = {62JXX (62KXX)}, MRNUMBER = {56 \#13457}, } @book {Graybill83, AUTHOR = {Graybill, F. A.}, TITLE = {Matrices with {A}pplications in {S}tatistics}, EDITION = {Second}, PUBLISHER = {Wadsworth Advanced Books and Software}, ADDRESS = {Belmont, Calif.}, YEAR = {1983}, PAGES = {xii+461}, ISBN = {0-534-98038-4}, MRCLASS = {15-01 (62J05)}, MRNUMBER = {83k:15001}, } @ARTICLE{GraybillMarsaglia57, author = {Graybill, F. A. and Marsaglia, G.}, title = {Idempotent matrices and quadratic forms in the general linear hypothesis}, journal = {Ann. Math. Statist.}, year = {1957}, volume = {28}, pages = {678--686}, keywords = {}, } @article {GraybillEtAl66, AUTHOR = {Graybill, F. A. and Meyer, Jr., C. D. and Painter, R. J.}, TITLE = {Note on the computation of the generalized inverse of a matrix}, JOURNAL = SIAMR, VOLUME = {8}, YEAR = {1966}, PAGES = {522--524}, MRCLASS = {15.15}, MRNUMBER = {35 \#1607}, } @ARTICLE{Green52, author = {Green, B.}, title = {The orthogonal approximation of an oblique structure in factor analysis}, journal = {Psychometrika}, year = {1952}, volume = {17}, pages = {429--440}, } @incollection {GreenMorley90, AUTHOR = {Green, W. L. and Morley, T. D.}, TITLE = {Operator means, norm convergence and matrix functions}, BOOKTITLE = {Signal {P}rocessing, {S}cattering and {O}perator {T}heory, and {N}umerical {M}ethods ({A}msterdam, 1989)}, PAGES = {551--556}, PUBLISHER = {Birkh\"auser Boston}, ADDRESS = {Boston, MA}, YEAR = {1990}, MRCLASS = {47A63 (15A60 47B15)}, MRNUMBER = {92k:47036}, } @article {GreenMorley90a, AUTHOR = {Green, W. L. and Morley, T. D.}, TITLE = {Operator means and matrix functions}, JOURNAL = LINAA1, VOLUME = {137/138}, YEAR = {1990}, PAGES = {453--465}, MRCLASS = {47A63 (47B15 47D99 47N70 93B25)}, MRNUMBER = {91i:47020}, } @article {Greensite99, AUTHOR = {Greensite, F.}, TITLE = {Second-order approximation of the pseudoinverse for operator deconvolutions and families of ill-posed problems}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {59}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--16 (electronic)}, MRCLASS = {65R30 (65J10)}, MRNUMBER = {99h:65222}, } @article {GreubRheinboldt59, AUTHOR = {Greub, W. and Rheinboldt, W. C.}, TITLE = {On a generalization of an inequality of {L}. {V}. {K}antorovich}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {10}, YEAR = {1959}, PAGES = {407--415}, MRCLASS = {46.00 (15.00)}, MRNUMBER = {21 \#3774}, } @ARTICLE{GreubRheinboldt60, author = {Greub, W. and Rheinboldt, W. C.}, title = {Non self--adjoint boundary value problems in ordinary differential equations}, journal = {J. Res. Nat. Bur. Standards Sect. B}, year = {64B}, volume = {1960}, pages = {83--90}, } @article{Greville57, author = {Greville, T. N. E.}, year = {1957}, title = {On smoothing a finite table: A matrix approach}, journal = {J. Soc. Indust. Appl. Math.}, volume = {5}, pages = {137--154}, } @article{Greville59, author = {Greville, T. N. E.}, year = {1959}, title = {The pseudoinverse of a rectangular matrix and its application to the solution of systems of linear equations}, journal = SIAMR, volume = {1}, pages = {38--43}, } @article{Greville60, author = {Greville, T. N. E.}, year = {1960}, title = {Some applications of the pseudoinverse of a matrix}, journal = SIAMR, volume = {2}, pages = {15--22}, } @article{Greville61, author = {Greville, T. N. E.}, year = {1961}, title = {Note on fitting functions of several independent variables}, journal = {J. Soc. Indust. Appl. Math.}, volume = {9}, pages = {109--115}, note = {(Erratum, \textit{ibid} \textbf{9}(1961), 317)}, } @article{Greville66, author = {Greville, T. N. E.}, year = {1966}, title = {Note on the generalized inverse of a matrix product}, journal = {J. Soc. Indust. Appl. Math.}, volume = {9}, pages = {109--115}, } @TECHREPORT{Greville67, author = {Greville, T. N. E.}, title = {Spectral generalized inverses of square matrices}, institution = {University of Wisconsin}, year = {1967}, type = {Math. Research Center Technical Summary Report}, number = {823}, address = {Madison, WI}, month = {October}, } @INPROCEEDINGS{Greville68, author = {Greville, T. N. E.}, crossref = {BoullionOdell68}, title = {Some new generalized inverses with spectral properties}, year = {1968}, pages = {26--46}, } @article {Greville73, AUTHOR = {Greville, T. N. E.}, TITLE = {The {S}ouriau-{F}rame algorithm and the {D}razin pseudoinverse}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {6}, YEAR = {1973}, PAGES = {205--208}, MRCLASS = {15A09}, MRNUMBER = {47 \#237}, } @article{Greville74, author = {Greville, T. N. E.}, year = {1974}, title = {Solutions of the Matrix Equation {$XAX = X$} and Relations between Oblique and Orthogonal Projectors}, journal = SIAJA, volume = {26}, pages = {828--832}, KEYWORDS = {proj, inv2}, } @incollection {GrevilleKeyfitz80, AUTHOR = {Greville, T. N. E. and Keyfitz, N.}, TITLE = {Backward population projection by a generalized inverse}, BOOKTITLE = {Computational {P}robability ({P}roc. {A}ctuarial {R}es. {C}onf., {B}rown {U}niv., {P}rovidence, {R.I.}, 1975)}, PAGES = {173--183}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1980}, MRCLASS = {92A15 (15A09)}, MRNUMBER = {82b:92031}, } @article {GriepentrogMarz89, AUTHOR = {Griepentrog, E. and M{\"a}rz, R.}, TITLE = {Basic properties of some differential-algebraic equations}, JOURNAL = {Z. Anal. Anwendungen}, FJOURNAL = {Zeitschrift f\"ur Analysis und Ihre Anwendungen}, VOLUME = {8}, YEAR = {1989}, NUMBER = {1}, PAGES = {25--41}, MRCLASS = {34A08}, MRNUMBER = {90d:34004}, } @article {Groetsch74, AUTHOR = {Groetsch, C. W.}, TITLE = {Steepest descent and least squares solvability}, JOURNAL = {Canad. Math. Bull.}, VOLUME = {17}, YEAR = {1974}, PAGES = {275--276}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {50 \#15326}, } @article {Groetsch75, AUTHOR = {Groetsch, C. W.}, TITLE = {A product integral representation of the generalized inverse}, JOURNAL = {Comment. Math. Univ. Carolinae}, VOLUME = {16}, YEAR = {1975}, PAGES = {13--20}, MRCLASS = {47A60}, MRNUMBER = {52 \#11638}, } @article {Groetsch75a, AUTHOR = {Groetsch, C. W.}, TITLE = {Representations of the generalized inverse}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {49}, YEAR = {1975}, PAGES = {154--157}, MRCLASS = {}, MRNUMBER = {50 \#14319}, } @book {Groetsch77, AUTHOR = {Groetsch, C. W.}, TITLE = {Generalized {I}nverses of {L}inear {O}perators: {R}epresentation and {A}pproximation. Monographs and Textbooks in Pure and Applied Mathematics, No. 37}, PUBLISHER = {Marcel Dekker Inc.}, ADDRESS = {New York}, YEAR = {1977}, PAGES = {viii+165}, MRCLASS = {65J05 (65F20)}, MRNUMBER = {56 \#17059}, } @article {Groetsch78, AUTHOR = {Groetsch, C. W.}, TITLE = {The {F}orsythe-{M}otzkin method for singular linear operator equations}, JOURNAL = {J. Optim. Theory Appl.}, VOLUME = {25}, YEAR = {1978}, NUMBER = {2}, PAGES = {311--315}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {58 \#8232}, } @article {Groetsch79, AUTHOR = {Groetsch, C. W.}, TITLE = {On rates of convergence for approximations to the generalized inverse}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = {Numerical Functional Analysis and Optimization}, VOLUME = {1}, YEAR = {1979}, NUMBER = {2}, PAGES = {195--201}, MRCLASS = {65J10 (47A50)}, MRNUMBER = {80b:65072}, } @article {Groetsch80, AUTHOR = {Groetsch, C. W.}, TITLE = {Generalized inverses and generalized splines}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = {Numerical Functional Analysis and Optimization}, VOLUME = {2}, YEAR = {1980}, NUMBER = {1}, PAGES = {93--97}, MRCLASS = {65J05 (47A05)}, MRNUMBER = {81j:65072}, KEYWORDS = {Splines, Hilbert}, NOTE = {(connection between generalized inverses and generalized splines, see \cite{Sard73})}, } @book {Groetsch84, AUTHOR = {Groetsch, C. W.}, TITLE = {The {T}heory of {T}ikhonov {R}egularization for {F}redholm {E}quations of the {F}irst {K}ind}, PUBLISHER = {Pitman}, ADDRESS = {London}, YEAR = {1984}, MRCLASS = {}, MRNUMBER = {}, } @article {Groetsch92, AUTHOR = {Groetsch, C. W.}, TITLE = {Spectral methods for linear inverse problems with unbounded operators}, JOURNAL = {J. Approx. Theory}, VOLUME = {70}, YEAR = {1992}, NUMBER = {1}, PAGES = {16--28}, MRCLASS = {47A50 (47A05 65J10)}, MRNUMBER = {93g:47011}, } @incollection {Groetsch93, AUTHOR = {Groetsch, C. W.}, TITLE = {Inclusions for the {M}oore-{P}enrose inverse with applications to computational methods}, BOOKTITLE = {Contributions in {N}umerical {M}athematics}, PAGES = {203--211}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1993}, MRCLASS = {65J20 (15A09 47A05 47A50)}, MRNUMBER = {95h:65041}, } @book {Groetsch93a, AUTHOR = {Groetsch, C. W.}, TITLE = {Inverse {P}roblems in the {M}athematical {S}ciences}, PUBLISHER = {Friedr. Vieweg \& Sohn}, ADDRESS = {Braunschweig}, YEAR = {1993}, PAGES = {vi+152}, ISBN = {3-528-06545-1}, MRCLASS = {00A69 (35-02 35R25 35R30 45A05 47B07 65J20)}, MRNUMBER = {94m:00008}, } @article {Groetsch95, AUTHOR = {Groetsch, C. W.}, TITLE = {Inclusions and identities for the {M}oore-{P}enrose inverse of a closed linear operator}, JOURNAL = {Math. Nachr.}, VOLUME = {171}, YEAR = {1995}, PAGES = {157--164}, MRCLASS = {47A05 (15A09)}, MRNUMBER = {96a:47004}, KEYWORDS = {spacH, invMP, linop}, } @article {GroetschGuacaneme87, AUTHOR = {Groetsch, C. W. and Guacaneme, J.}, TITLE = {Arcangeli's method for {F}redholm equations of the first kind}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {99}, YEAR = {1987}, NUMBER = {2}, PAGES = {256--260}, MRCLASS = {}, MRNUMBER = {88a:45016}, } @article {GroetschHanke96, AUTHOR = {Groetsch, C. W. and Hanke, M.}, TITLE = {A general framework for regularized evaluation of unstable operators}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {203}, YEAR = {1996}, NUMBER = {2}, PAGES = {451--463}, MRCLASS = {}, MRNUMBER = {97f:65037}, } @inproceedings{GroetschJacobs82, AUTHOR = {Groetsch, C. W. and Jacobs, B. J.}, TITLE = {Iterative methods for generalized inverses based on functional interpolation}, CROSSREF = {Campbell82a}, PAGES = {220--232}, YEAR = {1982}, MRCLASS = {65J10 (47A05)}, MRNUMBER = {84c:65081}, KEYWORDS = {aprx, spacH, compit}, } @article {GroetschKing79, AUTHOR = {Groetsch, C. W. and King, J. T.}, TITLE = {Extrapolation and the method of regularization for generalized inverses}, JOURNAL = {J. Approx. Theory}, VOLUME = {25}, YEAR = {1979}, NUMBER = {3}, PAGES = {233--247}, MRCLASS = {65J10 (47A05)}, MRNUMBER = {80e:65057}, } @article {GroetschNeubauer89, AUTHOR = {Groetsch, C. W. and Neubauer, A.}, TITLE = {Regularization of ill-posed problems: optimal parameter choice in finite dimensions}, JOURNAL = {J. Approx. Theory}, VOLUME = {58}, YEAR = {1989}, NUMBER = {2}, PAGES = {184--200}, MRCLASS = {}, MRNUMBER = {90j:65083}, } @article {GroetschScherzer93, AUTHOR = {Groetsch, C. W. and Scherzer, O.}, TITLE = {The optimal order of convergence for stable evaluation of differential operators}, JOURNAL = {Electronic J. Diff. Eqtns.}, VOLUME = {1993}, YEAR = {1993}, NUMBER = {4}, PAGES = {1--10}, MRCLASS = {}, MRNUMBER = {}, } @article {GroetschVogel87, AUTHOR = {Groetsch, C. W. and Vogel, C. R.}, TITLE = {Asymptotic theory of filtering for linear operator equations with discrete noisy data}, JOURNAL = {Math. Comp.}, VOLUME = {49}, YEAR = {1987}, NUMBER = {180}, PAGES = {499--506}, MRCLASS = {}, MRNUMBER = {88j:65123}, } @article {Grone80, AUTHOR = {Grone, R.}, TITLE = {Certain isometries of rectangular complex matrices}, JOURNAL = LINAA1, VOLUME = {29}, YEAR = {1980}, PAGES = {161--171}, MRCLASS = {15A60}, MRNUMBER = {81d:15007}, } @article {GroneEtAl87, AUTHOR = {Grone, R. and Johnson, C. R. and Sa, E. M. and Wolkowicz, H.}, TITLE = {Normal matrices}, JOURNAL = LINAA1, VOLUME = {87}, YEAR = {1987}, PAGES = {213--225}, MRCLASS = {15A57}, MRNUMBER = {88a:15045}, NOTE = {(characterizations of normal matrices, continued in \cite{ElsnerIkramov98})}, } @article {Gross97, AUTHOR = {Gro{\ss}, J.}, TITLE = {Some remarks concerning the reverse order law}, JOURNAL = {Discuss. Math. Algebra Stochastic Methods}, FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods}, VOLUME = {17}, YEAR = {1997}, NUMBER = {2}, PAGES = {135--141}, MRCLASS = {15A09}, MRNUMBER = {99g:15004}, } @article {Gross97a, AUTHOR = {Gro{\ss}, J.}, TITLE = {Special generalized inverse matrices connected with the theory of unified least squares}, JOURNAL = LINAA1, VOLUME = {264}, YEAR = {1997}, PAGES = {325--327}, MRCLASS = {62J05 (15A09)}, MRNUMBER = {1 465 874}, } @article {Gross97b, AUTHOR = {Gro{\ss}, J.}, TITLE = {A note on a partial ordering in the set of {H}ermitian matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {18}, YEAR = {1997}, NUMBER = {4}, PAGES = {887--892}, MRCLASS = {15A57}, MRNUMBER = {98i:15027}, } @article {Gross98, AUTHOR = {Gro{\ss}, J.}, TITLE = {More on concavity of a matrix function}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {19}, YEAR = {1998}, NUMBER = {2}, PAGES = {365--368 (electronic)}, MRCLASS = {15A09 (15A45 62J12)}, MRNUMBER = {98m:15010}, } @article {Gross98a, AUTHOR = {Gro{\ss}, J.}, TITLE = {On contractions in linear regression}, JOURNAL = {J. Statist. Plann. Inference}, VOLUME = {74}, YEAR = {1998}, NUMBER = {2}, PAGES = {343--351}, MRCLASS = {62J05 (62C15)}, MRNUMBER = {2000c:62099}, } @article {Gross99, AUTHOR = {Gro{\ss}, J.}, TITLE = {Solution to a rank equation}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {127--130}, MRCLASS = {15A24 (15A03)}, MRNUMBER = {99m:15011}, } @article {Gross99a, AUTHOR = {Gro{\ss}, J.}, TITLE = {Idempotency of the {H}ermitian part of a complex matrix}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {135--139}, MRCLASS = {15A24 (15A57)}, MRNUMBER = {2000c:15017}, } @article {Gross99b, AUTHOR = {Gro{\ss}, J.}, TITLE = {On the product of orthogonal projectors}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {141--150}, MRCLASS = {15A21 (15A57)}, MRNUMBER = {99k:15023}, } @article {Gross99d, AUTHOR = {Gro{\ss}, J.}, TITLE = {A note on the rank--subtractivity ordering}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {151--160}, MRCLASS = {}, MRNUMBER = {}, } @article {Gross99c, AUTHOR = {Gro{\ss}, J.}, TITLE = {On oblique projection, rank additivity and the {M}oore-{P}enrose inverse of the sum of two matrices}, JOURNAL = LINMA, VOLUME = {46}, YEAR = {1999}, NUMBER = {4}, PAGES = {265--275}, MRCLASS = {15A03 (15A09)}, MRNUMBER = {2000h:15002}, } @article {Gross00, AUTHOR = {Gro{\ss}, J.}, TITLE = {The {M}oore-{P}enrose inverse of a partitioned nonnegative definite matrix}, JOURNAL = LINAA1, VOLUME = {321}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {113--121}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {1 799 987}, } @article {Gross01, AUTHOR = {Gro{\ss}, J.}, TITLE = {Nonnegative-definite and positive-definite solutions to the matrix equation ${A}{X}{A}\sp \ast={B}$---revisited}, JOURNAL = LINAA1, VOLUME = {321}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {123--129}, MRCLASS = {15A24 (15A48)}, MRNUMBER = {1 799 988}, } @article {Gross01a, AUTHOR = {Gro{\ss}, J.}, TITLE = {L\"owner partial ordering and space preordering of {H}ermitian non-negative definite matrices}, JOURNAL = LINAA1, VOLUME = {326}, YEAR = {2001}, NUMBER = {1-3}, PAGES = {215--223}, MRCLASS = {15A48 (15A57 47A63)}, MRNUMBER = {1 815 961}, } @article {GrossEtAl97, AUTHOR = {Gro{\ss}, J. and Hauke, J. and Markiewicz, A.}, TITLE = {Some comments on matrix partial orderings}, JOURNAL = {Discuss. Math. Algebra Stochastic Methods}, FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods}, VOLUME = {17}, YEAR = {1997}, NUMBER = {2}, PAGES = {203--214}, MRCLASS = {15A45}, MRNUMBER = {99i:15026}, KEYWORDS = {Partial order}, } @article {GrossEtAl99, AUTHOR = {Gro{\ss}, J. and Hauke, J. and Markiewicz, A.}, TITLE = {Partial orderings, preorderings, and the polar decomposition of matrices}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {161--168}, MRCLASS = {15A45}, MRNUMBER = {2001b:15026}, } @article {GrossPuntanen00, AUTHOR = {Gro{\ss}, J. and Puntanen, S.}, TITLE = {Estimation under a general partitioned linear model}, JOURNAL = LINAA1, VOLUME = {321}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {131--144}, MRCLASS = {62J05 (62H12)}, MRNUMBER = {1 799 989}, } @article {GrossTrenkler96, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {On the least squares distance between affine subspaces}, JOURNAL = LINAA1, VOLUME = {237/238}, YEAR = {1996}, PAGES = {269--276}, MRCLASS = {51K99 (15A09 51N10)}, MRNUMBER = {97a:51024}, } @article {GrossTrenkler97, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {Generalized and hypergeneralized projectors}, JOURNAL = LINAA1, VOLUME = {264}, YEAR = {1997}, PAGES = {463--474}, MRCLASS = {15A09 (15A24 15A57)}, MRNUMBER = {98h:15004}, } @article {GrossTrenkler97a, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {On the equality of usual and {A}memiya's partially generalized least squares estimator}, JOURNAL = {Comm. Statist. Theory Methods}, VOLUME = {26}, YEAR = {1997}, NUMBER = {9}, PAGES = {2075--2086}, MRCLASS = {62J05}, MRNUMBER = {99c:62178}, } @article {GrossTrenkler97b, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {Restrictions and projections in linear regression}, JOURNAL = {Internat. J. Math. Ed. Sci. Tech.}, FJOURNAL = {International Journal of Mathematical Education in Science and Technology}, VOLUME = {28}, YEAR = {1997}, NUMBER = {3}, PAGES = {465--468}, MRCLASS = {62J05}, MRNUMBER = {98c:62125}, } @article {GrossTrenkler98, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {On the product of oblique projectors}, JOURNAL = LINMA, VOLUME = {44}, YEAR = {1998}, NUMBER = {3}, PAGES = {247--259}, MRCLASS = {15A27 (15A09)}, MRNUMBER = {99j:15023}, } @article {GrossTrenkler99, AUTHOR = {Gro{\ss}, J. and Trenkler, G.}, TITLE = {Nonsingularity of the difference of two oblique projectors}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {21}, YEAR = {1999}, NUMBER = {2}, PAGES = {390--395 (electronic)}, MRCLASS = {15A03}, MRNUMBER = {2000h:15003}, } @article {GrossEtAl99a, AUTHOR = {Gro{\ss}, J. and Trenkler, G. and Troschke, S. {-O.}}, TITLE = {On semi-orthogonality and a special class of matrices}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {169--182}, MRCLASS = {15A24 (15A03 15A63 62J05)}, MRNUMBER = {99m:15013}, } @article {GrossTroschke97, AUTHOR = {Gro{\ss}, J. and Troschke, S. {-O.}}, TITLE = {Some remarks on partial orderings of nonnegative definite matrices}, JOURNAL = LINAA1, VOLUME = {264}, YEAR = {1997}, PAGES = {457--461}, MRCLASS = {15A48 (62J05)}, MRNUMBER = {98i:15024}, } @preamble{ "\def\polhk#1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} " } @article {Gruszczynski81, AUTHOR = {Gruszczy{\'n}ski, M.}, TITLE = {The {M}oore-{P}enrose matrix inversion and estimation under additional constraints}, JOURNAL = {Przegl\polhk ad Statyst.}, FJOURNAL = {Polska Akademia Nauk. Komitet Statystyki i Ekonometrii. Przegl\polhk ad Statystyczny}, VOLUME = {28}, YEAR = {1981}, NUMBER = {3-4}, PAGES = {311--319 (1982)}, MRCLASS = {62J05 (15A09)}, MRNUMBER = {85g:62114}, } @article {Gu01, AUTHOR = {Gu, Chuanqing}, TITLE = {Generalized inverse matrix {P}ad\'e approximation on the basis of scalar products}, JOURNAL = LINAA1, VOLUME = {322}, YEAR = {2001}, NUMBER = {1-3}, PAGES = {141--167}, MRCLASS = {65D15 (41A21)}, MRNUMBER = {1 804 118}, } @article {GuacanemeOgden88, AUTHOR = {Guacaneme, J. and Ogden, R. D.}, TITLE = {On condition numbers and convergence of the alternating projections method}, JOURNAL = {Houston J. Math.}, VOLUME = {14}, YEAR = {1988}, NUMBER = {2}, PAGES = {209--217}, MRCLASS = {}, MRNUMBER = {90a:65128}, } @article {GuanEtAl94, AUTHOR = {Guan, Zhi Hong and Wen, Xiang Cai and Liu, Yong Qing}, TITLE = {Variation of the parameters formula and the problem of {B}{I}{B}{O} for singular measure differential systems with impulse effect}, JOURNAL = {Appl. Math. Comput.}, FJOURNAL = {Applied Mathematics and Computation}, VOLUME = {60}, YEAR = {1994}, NUMBER = {2-3}, PAGES = {153--169}, MRCLASS = {93C30 (34A30 34A37 34H05 93C57)}, MRNUMBER = {95c:93050}, } @article {GudderNeumann78, AUTHOR = {Gudder, S. P. and Neumann, M.}, TITLE = {Splittings and iterative methods for approximate solutions to singular operator equations in {H}ilbert spaces}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {62}, YEAR = {1978}, NUMBER = {2}, PAGES = {272--294}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {58 \#3408}, } @article {Guest50, AUTHOR = {Guest, P. G.}, TITLE = {Orthogonal polynomials in the least squares fitting of observations}, JOURNAL = {Philos. Mag. (7)}, VOLUME = {41}, YEAR = {1950}, PAGES = {124--137}, MRCLASS = {65.0X}, MRNUMBER = {11,692e}, } @BOOK{Guillemin63, author = {Guillemin, E. A.}, title = {Theory of {L}inear {P}hysical {S}ystems}, publisher = {Wiley}, year = {1963}, address = {New York}, } @article{Gulliksson95, author = {Gulliksson, M. E.}, year = {1995}, title = {On Modified {Gram--Schmidt} for Weighted and Constrained Linear Least Squares}, journal = {BIT}, volume = {35}, pages = {458--473}, } @article {GullikssonEtAl00, AUTHOR = {Gulliksson, M. E. and Wedin, P.-{\AA}. and Wei, Yimin}, TITLE = {Perturbation identities for regularized {T}ikhonov inverses and weighted pseudoinverses}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {40}, YEAR = {2000}, NUMBER = {3}, PAGES = {513--523}, MRCLASS = {65F20 (65J20)}, MRNUMBER = {1 780 405}, } @article{Gupta71, author = {N. N. Gupta}, year = {1971}, title = {An Iterative Method for Computation of Generalized Inverse and Matrix Rank}, journal = IEETS2, volume = {}, pages = {89--90}, KEYWORDS = {compit, ginv}, } @article{Gupta72, author = {N. N. Gupta}, year = {1972}, title = {An Optimum Iterative Method for the Computation of Matrix Rank}, journal = IEETS2, volume = {}, pages = {437--438}, KEYWORDS = {compit, ginv, iter, rank determination}, } @article {Guterman01, AUTHOR = {Guterman, A.}, TITLE = {Linear preservers for matrix inequalities and partial orderings}, JOURNAL = LINAA1, VOLUME = {331}, YEAR = {2001}, PAGES = {75--87}, KEYWORDS = {Minus order, rank additivity, linear preservers}, } @article {Guterman01a, AUTHOR = {Guterman, A.}, TITLE = {Linear preservers for {D}razin star partial order}, JOURNAL = {Comm. in Algebra}, VOLUME = {}, YEAR = {2001}, PAGES = {}, KEYWORDS = {Minus order, rank additivity, linear preservers}, } @article {GuyerEtAl01, AUTHOR = {G{\"u}yer, T. and K{\i{y}}maz, O. and Bilgici, G. and Mirasyedio{\u{g}}lu, {\c{S}}.}, TITLE = {A new method for computing the solutions of differential equation systems using generalized inverse via {M}aple}, JOURNAL = {Appl. Math. Comput.}, VOLUME = {121}, YEAR = {2001}, NUMBER = {2-3}, PAGES = {291--299}, MRCLASS = {65Lxx}, MRNUMBER = {1 830 875}, } @article {Haberman75, AUTHOR = {Haberman, S. J.}, TITLE = {How much do {G}auss-{M}arkov and least square estimates differ? {A} coordinate-free approach}, JOURNAL = {Ann. Statist.}, VOLUME = {3}, YEAR = {1975}, NUMBER = {4}, PAGES = {982--990}, MRCLASS = {62J05}, MRNUMBER = {51 \#14437}, NOTE = {(extension of \cite{Kruskal68}}, } @article {Hall75, AUTHOR = {Hall, F. J.}, TITLE = {Generalized inverses of a bordered matrix of operators}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {29}, YEAR = {1975}, PAGES = {152--163}, MRCLASS = {47A10}, MRNUMBER = {51 \#8850}, } @article {Hall76, AUTHOR = {Hall, F. J.}, TITLE = {On the independence of blocks of generalized inverses of bordered matrices}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {14}, YEAR = {1976}, NUMBER = {1}, PAGES = {53--61}, MRCLASS = {15A09}, MRNUMBER = {56 \#8591}, } @article {HallHartwig76, AUTHOR = {Hall, F. J. and Hartwig, R. E.}, TITLE = {Further results on generalized inverses of partitioned matrices}, JOURNAL = SIAJA, VOLUME = {30}, YEAR = {1976}, NUMBER = {4}, PAGES = {617--624}, MRCLASS = {15A09}, MRNUMBER = {53 \#8090}, KEYWORDS = {matpar}, } @article {HallHartwig81, AUTHOR = {Hall, F. J. and Hartwig, R. E.}, TITLE = {Algebraic properties of governing matrices used in {C}es\`aro-{N}eumann iterations}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, FJOURNAL = {Acad\'emie de la R\'epublique Populaire Roumaine. Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees}, VOLUME = {26}, YEAR = {1981}, NUMBER = {7}, PAGES = {959--978}, MRCLASS = {15A09}, MRNUMBER = {82h:15004}, } @article {HallEtAl83, AUTHOR = {Hall, F. J. and Hartwig, R. E. and Katz, I. J. and Newman, M.}, TITLE = {Pseudosimilarity and partial unit regularity}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {33(108)}, YEAR = {1983}, NUMBER = {3}, PAGES = {361--372}, MRCLASS = {15A21 (15A33)}, MRNUMBER = {85c:15019}, } @article {HallKatz79, AUTHOR = {Hall, F. J. and Katz, I. J.}, TITLE = {On ranks of integral generalized inverses of integral matrices}, JOURNAL = LINMA, VOLUME = {7}, YEAR = {1979}, NUMBER = {1}, PAGES = {73--85}, MRCLASS = {15A09 (15A36)}, MRNUMBER = {80d:15004}, } @article {HallKatz80, AUTHOR = {Hall, F. J. and Katz, I. J.}, TITLE = {More on integral generalized inverses of integral matrices}, JOURNAL = LINMA, VOLUME = {9}, YEAR = {1980}, NUMBER = {3}, PAGES = {201--209}, MRCLASS = {15A36 (15A09)}, MRNUMBER = {83e:15018}, } @article {HallKatz81, AUTHOR = {Hall, F. J. and Katz, I. J.}, TITLE = {Nonnegative integral generalized inverses}, JOURNAL = LINAA1, VOLUME = {39}, YEAR = {1981}, PAGES = {23--39}, MRCLASS = {15A09 (15A36)}, MRNUMBER = {83j:15007}, } @article {HallMeyer75, AUTHOR = {Hall, F. J. and Meyer, Jr., C. D.}, TITLE = {Generalized inverses of the fundamental bordered matrix used in linear estimation}, JOURNAL = SANKA, VOLUME = {37}, YEAR = {1975}, NUMBER = {3}, PAGES = {428--438}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {55 \#10478}, NOTE = {(corrigendum in {\it Sankhy\=a Ser. A}\ {\bf 40}(1980), 399)} } @article {HallumEtAl84, AUTHOR = {Hallum, C. R. and Boullion, T. L. and Odell, P. L.}, TITLE = {Best linear estimation in the restricted general linear model}, JOURNAL = {Indust. Math.}, VOLUME = {34}, YEAR = {1984}, NUMBER = {1}, PAGES = {53--64}, MRCLASS = {62J05}, MRNUMBER = {86f:62105}, } @article {HallumEtAl73, AUTHOR = {Hallum, C. R. and Lewis, T. O. and Boullion, T. L.}, TITLE = {Estimation in the restricted general linear model with a positive semidefinite covariance matrix}, JOURNAL = {Comm. Statist.}, VOLUME = {1}, YEAR = {1973}, PAGES = {157--166}, MRCLASS = {62F10}, MRNUMBER = {47 \#6016}, } @BOOK{Halmos58, author = {Halmos, P. R.}, title = {Finite--{D}imensional {V}ector {S}paces}, publisher = {D. Van Nostrand, Co.}, year = {1958}, address = {Princeton}, edition = {2nd}, } @BOOK{Halmos67, author = {Halmos, P. R.}, title = {A {H}ilbert {S}pace {P}roblem {B}ook}, publisher = {D. Van Nostrand, Co.}, year = {1967}, address = {Princeton}, } @ARTICLE{HalmosMcLaughlin63, author = {Halmos, P. R. and McLaughlin, J. E.}, title = {Partial isometries}, journal = PACJM, year = {1963}, volume = {13}, pages = {585--596}, } @ARTICLE{HalmosWallen70, author = {Halmos, P. R. and Wallen, L. J.}, title = {Powers of partial isometries}, journal = {J. Math. Mech.}, year = {1970}, volume = {19}, pages = {657--663}, } @ARTICLE{Halperin37, author = {Halperin, I.}, title = {Closures and adjoints of linear differential operators}, journal = {Ann. of Math.}, year = {1937}, pages = {880--919}, } @incollection{Hamburger51, AUTHOR = {Hamburger, H.}, TITLE = {Non--symmetric operators in {H}ilbert space}, BOOKTITLE = {Proceedings {S}ymposium on {S}pectral {T}heory and {D}ifferential {P}roblems}, PAGES = {67--112}, PUBLISHER = {Oklahoma A\& M College}, ADDRESS = {Stillwater, OK}, YEAR = {1951}, } @article {Hanke92, AUTHOR = {Hanke, M.}, TITLE = {Regularization with differential operators: an iterative approach}, JOURNAL = {Numer. Funct. Anal. Optim.}, VOLUME = {13}, YEAR = {1992}, NUMBER = {5-6}, PAGES = {523--540}, MRCLASS = {}, MRNUMBER = {93j:65089}, } @Article{HankeNeumann90, author = {Hanke, M. and Neumann, M.}, title = {Preconditionings and Splittings for Rectangular Systems}, journal = {Numerische Mathematik}, volume = {57}, number = {1}, pages = {85--95}, year = {1990}, mrclass = {65F10 (65F35)}, mrnumber = {91d:65053}, keywords = {approximate solution; converge; fixed point operator; fixed point system; inconsistent; iterative methods; limit point; minimal norm least squares solution; powers; preconditioning; reconditionings; rectangular systems; semiiterative method; semiiterative methods; splittings; stipulations; weighted Moore-Penrose solution}, } @article {HankeNeumann93, AUTHOR = {Hanke, M. and Neumann, M.}, TITLE = {The geometry of the set of scaled projections}, JOURNAL = LINAA1, VOLUME = {190}, YEAR = {1993}, PAGES = {137--148}, MRCLASS = {15A03}, MRNUMBER = {94g:15002}, } @article {HankeNiethammer90, AUTHOR = {Hanke, M. and Niethammer, W.}, TITLE = {On the acceleration of {K}aczmarz's method for inconsistent linear systems}, JOURNAL = LINAA1, VOLUME = {130}, YEAR = {1990}, PAGES = {83--98}, MRCLASS = {}, MRNUMBER = {91f:65065}, KEYWORDS = {Image reconstruction from projections}, } @ARTICLE{HansenRobinson74, author = {Hansen, G. W. and Robinson, D. W.}, title = {On the existence of generalized inverses}, journal = LINAA1, year = {1974}, volume = {8}, pages = {95--104}, } @article{Hansen87, author = {P. C. Hansen}, year = {1987}, title = {The Truncated {SVD} as a Method for Regularization}, journal = {BIT}, volume = {27}, pages = {534--553}, note = {}, } @article {Hanson71, AUTHOR = {Hanson, R. J.}, TITLE = {A numerical method for solving {F}redholm integral equations of the first kind using singular values}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {8}, YEAR = {1971}, PAGES = {616--622}, MRCLASS = {65R05}, MRNUMBER = {45 \#2943}, } @article {HansonNorris81, AUTHOR = {Hanson, R. J. and Norris, M. J.}, TITLE = {Analysis of measurements based on the singular value decomposition}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, VOLUME = {2}, YEAR = {1981}, NUMBER = {3}, PAGES = {363--373}, MRCLASS = {65D10 (65F30)}, MRNUMBER = {82m:65011}, } @book {HarrisB66, AUTHOR = {Harris, B.}, TITLE = {Theory of {P}robability}, PUBLISHER = {Addison-Wesley}, ADDRESS = {Reading, Mass.}, YEAR = {1966}, PAGES = {ix+294}, MRCLASS = {60.00}, MRNUMBER = {34 \#6811}, KEYWORDS = {Probability}, } @article {HarrisHelvig66, AUTHOR = {Harris, Jr., W. A. and Helvig, T. N.}, TITLE = {Applications of the pseudoinverse to modeling}, JOURNAL = {Technometrics}, VOLUME = {8}, YEAR = {1966}, PAGES = {351--357}, MRCLASS = {62.55}, MRNUMBER = {34 \#8562}, } @article {Harte92, AUTHOR = {Harte, R.}, TITLE = {Polar decomposition and the {M}oore-{P}enrose inverse}, JOURNAL = {Panamer. Math. J.}, FJOURNAL = {Panamerican Mathematical Journal}, VOLUME = {2}, YEAR = {1992}, NUMBER = {4}, PAGES = {71--76}, MRCLASS = {47A05 (46K05 46L05 47C15)}, MRNUMBER = {93i:47003}, } @article {HarteMbekhta92, AUTHOR = {Harte, R. and Mbekhta, M.}, TITLE = {On generalized inverses in ${C}\sp *$-algebras}, JOURNAL = {Studia Math.}, FJOURNAL = {Studia Mathematica}, VOLUME = {103}, YEAR = {1992}, NUMBER = {1}, PAGES = {71--77}, MRCLASS = {46L05 (16U99 47A05 47D25)}, MRNUMBER = {93i:46097}, } @article {HarteMbekhta93, AUTHOR = {Harte, R. and Mbekhta, M.}, TITLE = {Generalized inverses in ${C}\sp *$-algebras. {I}{I}}, JOURNAL = {Studia Math.}, VOLUME = {106}, YEAR = {1993}, NUMBER = {2}, PAGES = {129--138}, MRCLASS = {46L05 (15A09 47A05 47D25)}, MRNUMBER = {94k:46113}, } @article {HartmannHartwig96, AUTHOR = {Hartmann, W. M. and Hartwig, R. E.}, TITLE = {Computing the {M}oore-{P}enrose inverse for the covariance matrix in constrained nonlinear estimation}, JOURNAL = SIAJO, VOLUME = {6}, YEAR = {1996}, NUMBER = {3}, PAGES = {727--747}, MRCLASS = {65F20 (65F10 65U05)}, MRNUMBER = {98i:65031}, } @incollection {Hartung76, AUTHOR = {Hartung, J.}, TITLE = {On a method for computing pseudoinverses}, BOOKTITLE = {Optimization and {O}perations {R}esearch ({P}roc. {C}onf., {O}berwolfach, 1975). {L}ecture {N}otes in {E}conom. {M}ath. {S}ystems, Vol. 117}, PAGES = {115--125}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1976}, MRCLASS = {65F20}, MRNUMBER = {56 \#9942}, } @article {Hartung77, AUTHOR = {Hartung, J.}, TITLE = {Zur {D}arstellung pseudoinverser {O}peratoren}, JOURNAL = {Arch. Math. (Basel)}, VOLUME = {28}, YEAR = {1977}, NUMBER = {2}, PAGES = {200--208}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {55 \#13769}, } @article {Hartung79, AUTHOR = {Hartung, J.}, TITLE = {A note on restricted pseudoinverses}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {10}, YEAR = {1979}, NUMBER = {2}, PAGES = {266--273}, MRCLASS = {47A05 (65J10)}, MRNUMBER = {80j:47004}, } @article {Hartung81, AUTHOR = {Hartung, J.}, TITLE = {Nonnegative minimum biased invariant estimation in variance component models}, JOURNAL = {Ann. Statist.}, FJOURNAL = {The Annals of Statistics}, VOLUME = {9}, YEAR = {1981}, NUMBER = {2}, PAGES = {278--292}, MRCLASS = {62J10}, MRNUMBER = {82e:62106}, } @article {HartungWerner80, AUTHOR = {Hartung, J. and Werner, H. {-J}.}, TITLE = {Zur {V}erwendung der restringierten {M}oore-{P}enrose-{I}nversen beim {T}esten von linearen {H}ypothesen}, JOURNAL = {Z. Angew. Math. Mech.}, FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten}, VOLUME = {60}, YEAR = {1980}, NUMBER = {7}, PAGES = {T344--T346}, MRCLASS = {62J05}, MRNUMBER = {82j:62052}, } @book {HartungWerner84, AUTHOR = {Hartung, J. and Werner, H. {-J}.}, TITLE = {Hypothesenpr\"ufung im restringierten linearen {M}odell. {T}heorie und {A}nwendungen (With English and French summaries)}, PUBLISHER = {Vandenhoeck \& Ruprecht}, ADDRESS = {G\"ottingen}, YEAR = {1984}, PAGES = {128}, ISBN = {3-525-11260-2}, MRCLASS = {62J05}, MRNUMBER = {86g:62101}, } @article {Hartwig75, AUTHOR = {Hartwig, R. E.}, TITLE = {$1$-$2$ inverses and the invariance of ${B}{A}\sp{+}{C}$}, JOURNAL = LINAA1, VOLUME = {11}, YEAR = {1975}, NUMBER = {3}, PAGES = {271--275}, MRCLASS = {15A09}, MRNUMBER = {51 \#12880}, KEYWORD = {inv1, inv2}, } @article {Hartwig75a, AUTHOR = {Hartwig, R. E.}, TITLE = {${A}{X}-{X}{B}={C}$, resultants and generalized inverses}, JOURNAL = SIAJA, VOLUME = {28}, YEAR = {1975}, PAGES = {154--183}, MRCLASS = {15A24}, MRNUMBER = {51 \#8143}, } @article {Hartwig76, AUTHOR = {Hartwig, R. E.}, TITLE = {Singular value decomposition and the {M}oore-{P}enrose inverse of bordered matrices}, JOURNAL = SIAJA, VOLUME = {31}, YEAR = {1976}, NUMBER = {1}, PAGES = {31--41}, MRCLASS = {15A09}, MRNUMBER = {53 \#10826}, KEYWORDS = {svd, invMP, matpar}, } @article {Hartwig76a, AUTHOR = {Hartwig, R. E.}, TITLE = {More on the {S}ouriau-{F}rame algorithm and the {D}razin inverse}, JOURNAL = SIAJA, VOLUME = {31}, YEAR = {1976}, NUMBER = {1}, PAGES = {42--46}, MRCLASS = {15A09}, MRNUMBER = {53 \#10827}, } @article {Hartwig76b, AUTHOR = {Hartwig, R. E.}, TITLE = {Rank factorization and {M}oore-{P}enrose inversion}, JOURNAL = {Indust. Math.}, VOLUME = {26}, YEAR = {1976}, NUMBER = {1}, PAGES = {49--63}, MRCLASS = {15A09}, MRNUMBER = {53 \#5625}, } @article {Hartwig76c, AUTHOR = {Hartwig, R. E.}, TITLE = {Block generalized inverses}, JOURNAL = {Arch. Rational Mech. Anal.}, VOLUME = {61}, YEAR = {1976}, NUMBER = {3}, PAGES = {197--251}, MRCLASS = {15A09 (16A28)}, MRNUMBER = {53 \#2975}, KEYWORDS = {matpar}, } @article {Hartwig77, AUTHOR = {Hartwig, R. E.}, TITLE = {Generalized inverses of special block matrices}, JOURNAL = {Bull. Calcutta Math. Soc.}, FJOURNAL = {Bulletin of the Calcutta Mathematical Society}, VOLUME = {69}, YEAR = {1977}, NUMBER = {6}, PAGES = {397--402}, MRCLASS = {15A09}, MRNUMBER = {81a:15008}, } @article {Hartwig78, AUTHOR = {Hartwig, R. E.}, TITLE = {Generalized inverses, ${E}{P}$ elements and associates}, JOURNAL = REVRM, VOLUME = {23}, YEAR = {1978}, NUMBER = {1}, PAGES = {57--60}, MRCLASS = {15A33}, MRNUMBER = {57 \#12556}, } @article {Hartwig78a, AUTHOR = {Hartwig, R. E.}, TITLE = {Spectral inverses and the row-space equations}, JOURNAL = LINAA1, VOLUME = {20}, YEAR = {1978}, NUMBER = {1}, PAGES = {57--68}, MRCLASS = {15A09}, MRNUMBER = {57 \#6048}, KEYWORDS = {Drazin inverse, existence, properties}, } @article {Hartwig78b, AUTHOR = {Hartwig, R. E.}, TITLE = {Schur's theorem and the {D}razin inverse}, JOURNAL = {Pacific J. Math.}, VOLUME = {78}, YEAR = {1978}, NUMBER = {1}, PAGES = {133--138}, MRCLASS = {15A09}, MRNUMBER = {80a:15004}, } @article {Hartwig78c, AUTHOR = {Hartwig, R. E.}, TITLE = {A note on the partial ordering of positive semidefinite matrices}, JOURNAL = LINMA, VOLUME = {6}, YEAR = {1978}, PAGES = {223--226}, MRCLASS = {}, MRNUMBER = {}, } @article {Hartwig79, AUTHOR = {Hartwig, R. E.}, TITLE = {A note on the existence of inner and outer inverses}, JOURNAL = {Math. Japon.}, FJOURNAL = {Mathematica Japonica}, VOLUME = {23}, YEAR = {1978/79}, NUMBER = {4}, PAGES = {339--343}, MRCLASS = {16A30 (16A32)}, MRNUMBER = {80g:16017}, } @article {Hartwig80, AUTHOR = {Hartwig, R. E.}, TITLE = {How to partially order regular elements}, JOURNAL = {Math. Japon.}, VOLUME = {25}, YEAR = {1980}, NUMBER = {1}, PAGES = {1--13}, MRCLASS = {06F05}, MRNUMBER = {81i:06014}, } @article {Hartwig80a, AUTHOR = {Hartwig, R. E.}, TITLE = {An application of the {M}oore-{P}enrose inverse to antisymmetric relations}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {78}, YEAR = {1980}, NUMBER = {2}, PAGES = {181--186}, MRCLASS = {16A28 (15A09)}, MRNUMBER = {82a:16016}, } @article {Hartwig81, AUTHOR = {Hartwig, R. E.}, TITLE = {A method for calculating ${A}\sp{d}$}, JOURNAL = {Math. Japon.}, VOLUME = {26}, YEAR = {1981}, NUMBER = {1}, PAGES = {37--43}, MRCLASS = {15A09}, MRNUMBER = {82h:15005}, } @article {Hartwig81a, AUTHOR = {Hartwig, R. E.}, TITLE = {A note on rank additivity}, JOURNAL = LINMA, VOLUME = {10}, YEAR = {1981}, PAGES = {59--61}, MRCLASS = {}, MRNUMBER = {}, } @article {Hartwig81b, AUTHOR = {Hartwig, R. E.}, TITLE = {Drazin inverses and canonical forms in ${M}\sb{n}({\bf {Z}}/h)$}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {37}, YEAR = {1981}, PAGES = {205--233}, MRCLASS = {15A09 (15A36)}, MRNUMBER = {82k:15005}, } @article {Hartwig82, AUTHOR = {Hartwig, R. E.}, TITLE = {Applications of the {W}ro\'nskian and {G}ram matrices of $\{t\sp{i}e\sp{\lambda \sb{k}t}\}$}, JOURNAL = LINAA1, VOLUME = {43}, YEAR = {1982}, PAGES = {229--241}, MRCLASS = {93B05 (15A15 34A30 34H05)}, MRNUMBER = {83f:93007}, } @article {Hartwig86, AUTHOR = {Hartwig, R. E.}, TITLE = {The reverse order law revisited}, JOURNAL = LINAA1, VOLUME = {76}, YEAR = {1986}, PAGES = {241--246}, MRCLASS = {15A09}, MRNUMBER = {87j:15009}, } @incollection {Hartwig87, AUTHOR = {Hartwig, R. E.}, TITLE = {The group inverse of a block triangular matrix}, BOOKTITLE = {Current {T}rends in {M}atrix {T}heory ({A}uburn, {A}la., 1986)}, PAGES = {137--146}, PUBLISHER = {North-Holland}, ADDRESS = {New York}, YEAR = {1987}, MRCLASS = {15A09 (15A57)}, KEYWORDS = {invgr, strm}, MRNUMBER = {88f:15007}, } @article {Hartwig87a, AUTHOR = {Hartwig, R. E.}, TITLE = {A remark on the characterization of the parallel sum of two matrices}, JOURNAL = LINMA, VOLUME = {22}, YEAR = {1987}, NUMBER = {2}, PAGES = {193--197}, MRCLASS = {15A09 (15A30 15A33)}, MRNUMBER = {89f:15006}, } @article {Hartwig93, AUTHOR = {Hartwig, R. E.}, TITLE = {The pyramid decomposition and rank minimization}, JOURNAL = LINAA1, VOLUME = {191}, YEAR = {1993}, PAGES = {53--76}, MRCLASS = {15A23}, MRNUMBER = {94j:15011}, } @article {Hartwig94, AUTHOR = {Hartwig, R. E.}, TITLE = {The weighted $*$-core-nilpotent decomposition}, JOURNAL = LINAA1, VOLUME = {211}, YEAR = {1994}, PAGES = {101--111}, MRCLASS = {15A09 (15A21)}, MRNUMBER = {95i:15004}, } @article {Hartwig94a, AUTHOR = {Hartwig, R. E.}, TITLE = {E{P} perturbations}, JOURNAL = {Sankhy\=a Ser. A}, FJOURNAL = {Sankhy\=a. The Indian Journal of Statistics. Series A}, VOLUME = {56}, YEAR = {1994}, NUMBER = {2}, PAGES = {347--357}, MRCLASS = {15A57 (15A09)}, MRNUMBER = {99j:15033}, } @article {HartwigDrazin82, AUTHOR = {Hartwig, R. E. and Drazin, M. P.}, TITLE = {Lattice properties of the * order for matrices}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {86}, YEAR = {1982}, PAGES = {359--378}, } @article {HartwigHall78, AUTHOR = {Hartwig, R. E. and Hall, F. J.}, TITLE = {Pseudo--similarity for matrices over a field}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {71}, YEAR = {1978}, NUMBER = {1}, PAGES = {6--10}, MRCLASS = {15A21}, MRNUMBER = {58 \#28027}, } @inproceedings{HartwigHall82, AUTHOR = {Hartwig, R. E. and Hall, F. J.}, TITLE = {Applications of the {D}razin inverse to {C}es\`aro--{N}eumann iterations}, CROSSREF = {Campbell82a}, PAGES = {145--195}, YEAR = {1982}, MRCLASS = {15A09}, MRNUMBER = {84a:15006}, KEYWORDS = {invD, compit, serexp}, } @article {HartwigKatz97, AUTHOR = {Hartwig, R. E. and Katz, I. J.}, TITLE = {On products of {E}{P} matrices}, JOURNAL = LINAA1, VOLUME = {252}, YEAR = {1997}, PAGES = {339--345}, MRCLASS = {15A57}, MRNUMBER = {98a:15050}, } @article {HartwigLevine81, AUTHOR = {Hartwig, R. E. and Levine, J.}, TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {III}}, JOURNAL = {Cryptologia}, VOLUME = {5}, YEAR = {1981}, NUMBER = {2}, PAGES = {67--77}, MRCLASS = {94B99}, MRNUMBER = {82j:94022a}, } @article {HartwigLevine81a, AUTHOR = {Hartwig, R. E. and Levine, J.}, TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {IV}}, JOURNAL = {Cryptologia}, VOLUME = {5}, YEAR = {1981}, NUMBER = {4}, PAGES = {213--228}, MRCLASS = {94B99}, MRNUMBER = {82j:94022b}, } @article {HartwigLuh77, AUTHOR = {Hartwig, R. E. and Luh, Jiang}, TITLE = {A note on the group structure of unit regular ring elements}, JOURNAL = PACJM, VOLUME = {71}, YEAR = {1977}, NUMBER = {2}, PAGES = {449--461}, MRCLASS = {16A30}, MRNUMBER = {56 \#407}, KEYWORDS = {algr}, } @article {HartwigLuh81, AUTHOR = {Hartwig, R. E. and Luh, Jiang}, TITLE = {Unitary regular rings and partial isometry rings}, JOURNAL = {Math. Japon.}, FJOURNAL = {Mathematica Japonica}, VOLUME = {26}, YEAR = {1981}, NUMBER = {4}, PAGES = {401--413}, MRCLASS = {16A30 (16A28)}, MRNUMBER = {83b:16008}, } @article {HartwigSemrl99, AUTHOR = {Hartwig, R. E. and {\v{S}}emrl, P.}, TITLE = {Power additivity and orthogonality}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {20}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--13 (electronic)}, MRCLASS = {15A21 (15A24)}, MRNUMBER = {99f:15016}, } @article {HartwigShoaf77, AUTHOR = {Hartwig, R. E. and Shoaf, J. M.}, TITLE = {Group inverses and {D}razin inverses of bidiagonal and triangular {T}oeplitz matrices}, JOURNAL = JAUSMA, VOLUME = {24}, YEAR = {1977}, NUMBER = {1}, PAGES = {10--34}, MRCLASS = {15A09}, MRNUMBER = {57 \#3150}, KEYWORDS = {invD, invgr}, } @article {HartwigShoaf79, AUTHOR = {Hartwig, R. E. and Shoaf, J. M.}, TITLE = {On the derivative of the {D}razin inverse of a complex matrix}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {10}, YEAR = {1979}, NUMBER = {1}, PAGES = {207--216}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {80b:65050}, } @article {HartwigShoaf80, AUTHOR = {Hartwig, R. E. and Shoaf, J. M.}, TITLE = {Invariance, group inverses and parallel sums}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, FJOURNAL = {Acad\'emie de la R\'epublique Populaire Roumaine. Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees}, VOLUME = {25}, YEAR = {1980}, NUMBER = {1}, PAGES = {33--42}, MRCLASS = {16A30}, MRNUMBER = {82e:16007}, } @article {HartwigStyan86, AUTHOR = {Hartwig, R. E. and Styan, G. P. H.}, TITLE = {On some characterizations of the star partial orderings and rank subtractivity}, JOURNAL = LINAA1, VOLUME = {82}, YEAR = {1986}, PAGES = {145--161}, MRCLASS = {}, MRNUMBER = {}, } @article {HartwigEtAl96, AUTHOR = {Hartwig, R. E. and Omladi{\v{c}}, M. and {\v{S}}emrl, P. and Styan, G. P. H.}, TITLE = {On some characterizations of pairwise star ortogonality using rank and dagger additivity and subtractivity}, JOURNAL = LINAA1, VOLUME = {237--238}, YEAR = {1996}, PAGES = {499--507}, MRCLASS = {}, MRNUMBER = {}, } @article {HartwigEtAl01, AUTHOR = {Hartwig, R. E. and Wang, Guorong and Wei, Yimin}, TITLE = {Some additive results on {D}razin inverse}, JOURNAL = LINAA1, VOLUME = {322}, YEAR = {2001}, NUMBER = {1-3}, PAGES = {207--217}, MRCLASS = {15A09}, MRNUMBER = {1 804 521}, } @article {Harville76, AUTHOR = {Harville, D. A.}, TITLE = {Extension of the {G}auss-{M}arkov theorem to include the estimation of random effects}, JOURNAL = {Ann. Statist.}, VOLUME = {4}, YEAR = {1976}, NUMBER = {2}, PAGES = {384--395}, MRCLASS = {62J05}, MRNUMBER = {53 \#1862}, } @article {Harville96, AUTHOR = {Harville, D. A.}, TITLE = {Generalized inverses and ranks of modified matrices}, JOURNAL = {J. Indian Soc. Agricultural Statist.}, VOLUME = {49}, YEAR = {1996/97}, PAGES = {67--78, iv}, MRCLASS = {15A09}, MRNUMBER = {98f:15001}, } @book {Harville97, AUTHOR = {Harville, D. A.}, TITLE = {Matrix {A}lgebra from a {S}tatistician's {P}erspective}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xviii+630}, ISBN = {0-387-94978-X}, MRCLASS = {15-01}, MRNUMBER = {98k:15001}, } @article {HarwoodEtAl70, AUTHOR = {Harwood, W. R. and Lovass--Nagy, V. and Powers, D. L.}, TITLE = {A note on the generalized inverses of some partitioned matrices}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {19}, YEAR = {1970}, PAGES = {555--559}, MRCLASS = {65.35 (15.00)}, MRNUMBER = {42 \#7048}, } @article {Haussler78, AUTHOR = {H{\"a}ussler, W. M.}, TITLE = {Zu \"uber- und unterrelaxierten {N}ewton-{V}erfahren}, JOURNAL = {Z. Angew. Math. Mech.}, FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten}, VOLUME = {58}, YEAR = {1978}, NUMBER = {7}, PAGES = {T421--T423}, MRCLASS = {65H05}, MRNUMBER = {80g:65053}, } @article {HawkinsBradu90, AUTHOR = {Hawkins, D. M. and Bradu, D.}, TITLE = {Application of the {M}oore-{P}enrose inverse of a data matrix in multiple regression}, JOURNAL = LINAA1, VOLUME = {127}, YEAR = {1990}, PAGES = {403--425}, MRCLASS = {62J05 (62J20)}, MRNUMBER = {91f:62117}, } @article {HawkinsBen-Israel73, AUTHOR = {Hawkins, J. B. and Ben-Israel, A.}, TITLE = {On generalized matrix functions}, JOURNAL = LINMA, VOLUME = {1}, YEAR = {1973}, NUMBER = {2}, PAGES = {163--171}, MRCLASS = {15A15}, MRNUMBER = {48 \#8523}, KEYWORDS = {matfun}, } @article {Haynsworth70, AUTHOR = {Haynsworth, E. V.}, TITLE = {Applications of an inequality for the {S}chur complement}, JOURNAL = PROAM, VOLUME = {24}, YEAR = {1970}, PAGES = {512--516}, KEYWORDS = {Schur complement}, } @article {HaynsworthWall79, AUTHOR = {Haynsworth, E. V. and Wall, J. R.}, TITLE = {Group inverses of certain nonnegative matrices}, JOURNAL = LINAA1, VOLUME = {25}, YEAR = {1979}, PAGES = {271--288}, MRCLASS = {15A09}, MRNUMBER = {80b:15006}, } @article {HaynsworthWall81, AUTHOR = {Haynsworth, E. V. and Wall, J. R.}, TITLE = {Group inverses of certain positive operators}, JOURNAL = LINAA1, VOLUME = {40}, YEAR = {1981}, PAGES = {143--159}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {82j:15004}, } @article {HaukeMarkiewicz95, AUTHOR = {Hauke, J. and Markiewicz, A.}, TITLE = {On partial orderings on the set of rectangular matrices and their properties}, JOURNAL = {Discuss. Math. Algebra Stochastic Methods}, FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods}, VOLUME = {15}, YEAR = {1995}, NUMBER = {1}, PAGES = {5--10}, MRCLASS = {15A99}, MRNUMBER = {96k:15018}, KEYWORDS = {Partial orders, matrix functions}, } @article {HaukeMarkiewicz95a, AUTHOR = {Hauke, J. and Markiewicz, A.}, TITLE = {On partial orderings on the set of rectangular matrices}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {219}, YEAR = {1995}, PAGES = {187--193}, MRCLASS = {15A48}, MRNUMBER = {96c:15033}, KEYWORDS = {Partial orders, matrix functions}, NOTE = {(see \cite{Markiewicz99})}, } @article {Hearon67, AUTHOR = {Hearon, J. Z.}, TITLE = {On the singularity of a certain bordered matrix}, JOURNAL = SIAJA, VOLUME = {15}, YEAR = {1967}, PAGES = {1413--1421}, MRCLASS = {15.15}, MRNUMBER = {37 \#225}, } @article {Hearon67a, AUTHOR = {Hearon, J. Z.}, TITLE = {Polar factorization of a matrix}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {71B}, YEAR = {1967}, PAGES = {65--67}, MRCLASS = {15.15}, MRNUMBER = {37 \#1382}, } @article {Hearon67aa, AUTHOR = {Hearon, J. Z.}, TITLE = {Construction of ${\rm {E}{P}r}$ generalized inverses by inversion of nonsingular matrices}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {71B}, YEAR = {1967}, PAGES = {57--60}, MRCLASS = {15.15 (65.00)}, MRNUMBER = {36 \#6425}, } @article {Hearon67aaa, AUTHOR = {Hearon, J. Z.}, TITLE = {A generalized matrix version of {R}ennie's inequality}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {71B}, YEAR = {1967}, PAGES = {61--64}, MRCLASS = {15.58}, MRNUMBER = {37 \#232}, } @article {Hearon67b, AUTHOR = {Hearon, J. Z.}, TITLE = {Partially isometric matrices}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {71B}, YEAR = {1967}, PAGES = {225--228}, MRCLASS = {15.30}, MRNUMBER = {37 \#2779}, } @article {Hearon67c, AUTHOR = {Hearon, J. Z.}, TITLE = {Symmetrizable generalized inverses of symmetrizable matrices}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {71B}, YEAR = {1967}, PAGES = {229--231}, MRCLASS = {15.15}, MRNUMBER = {37 \#2770}, } @article {Hearon68, AUTHOR = {Hearon, J. Z.}, TITLE = {Generalized inverses and solutions of linear systems}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {72B}, YEAR = {1968}, PAGES = {303--308}, MRCLASS = {15.15}, MRNUMBER = {39 \#224}, } @article {HearonEvans68, AUTHOR = {Hearon, J. Z. and Evans, J. W.}, TITLE = {On spaces and maps of generalized inverses}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {72B}, YEAR = {1968}, PAGES = {103--107}, MRCLASS = {15.15}, MRNUMBER = {38 \#4493}, } @article {HearonEvans68a, AUTHOR = {Hearon, J. Z. and Evans, J. W.}, TITLE = {Differentiable generalized inverses}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {72B}, YEAR = {1968}, PAGES = {109--113}, MRCLASS = {15.15}, KEYWORDS = {alglin, pert, invMP, matder}, MRNUMBER = {38 \#4494}, } @article {Hedman99, AUTHOR = {Hedman, B. A.}, TITLE = {An earlier date for ``{C}ramer's rule''}, JOURNAL = {Historia Math.}, FJOURNAL = {Historia Mathematica}, VOLUME = {26}, YEAR = {1999}, NUMBER = {4}, PAGES = {365--368}, MRCLASS = {01A50}, MRNUMBER = {2000i:01020}, NOTE = {(Cramer's rule was discovered by Maclaurin 20 years earlier)}, } @article {HeilWalnut89, AUTHOR = {Heil, C. and Walnut, D.}, TITLE = {Continuous and discrete wavelet transforms}, JOURNAL = SIAMR, VOLUME = {31}, YEAR = {1989}, PAGES = {628--666}, MRCLASS = {}, MRNUMBER = {91c:42032}, } @article {Heinig97, AUTHOR = {Heinig, G.}, TITLE = {The group inverse of the transformation ${S}({X})={A}{X}-{X}{B}$}, JOURNAL = LINAA1, VOLUME = {257}, YEAR = {1997}, PAGES = {321--342}, MRCLASS = {15A09 (15A04)}, MRNUMBER = {98c:15014}, } @Article{HeinigHellinger93, author = {Heinig, G. and Hellinger, F.}, title = {On the {Bezoutian} Structure of the {Moore--Penrose} Inverses of {Hankel} Matrices}, journal = {SIAM Journal on Matrix Analysis and Applications}, volume = {14}, number = {3}, pages = {629--645}, year = {1993}, mrclass = {15A09 (15A57 47A05 47B35)}, mrnumber = {94f:15006}, } @article {HeinigHellinger93a, AUTHOR = {Heinig, G. and Hellinger, F.}, TITLE = {Displacement structure of generalized inverse matrices}, JOURNAL = lINAA1, VOLUME = {211}, YEAR = {1994}, PAGES = {67--83}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {95h:15006}, } @Article{HeinigHellinger94, author = {Heinig, G. and Hellinger, F.}, title = {{Moore-Penrose} Inversion of Square {Toeplitz} Matrices}, journal = {SIAM Journal on Matrix Analysis and Applications}, volume = {15}, number = {2}, pages = {418--450}, year = {1994}, mrclass = {15A09 (47A05 47A50 65F20)}, mrnumber = {95c:15008}, url = {http://epubs.siam.org/sam-bin/dbq/article/22585}, } @article {HeinigHellinger94a, AUTHOR = {Heinig, G. and Hellinger, F.}, TITLE = {Displacement structure of pseudoinverses}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {197/198}, YEAR = {1994}, PAGES = {623--649}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {47A05 (15A09)}, MRNUMBER = {95f:47004}, } @article {HeinigHellinger94b, AUTHOR = {Heinig, G. and Hellinger, F.}, TITLE = {Displacement structure of generalized inverse matrices}, JOURNAL = LINAA1, VOLUME = {211}, YEAR = {1994}, PAGES = {67--83}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {95h:15006}, } @article{Helton68, author = {B. W. Helton}, year = {1968}, title = {Logarithms of Matrices}, journal = {Proceedings of the American Mathematical Society}, volume = {19}, pages = {733--736}, } @article {HendersonSearle80, AUTHOR = {Henderson, H. V. and Searle, S. R.}, TITLE = {The vec-permutation matrix, the vec operator and {K}ronecker products: a review}, JOURNAL = LINMA, VOLUME = {9}, YEAR = {1980/81}, NUMBER = {4}, PAGES = {271--288}, MRCLASS = {15A24}, MRNUMBER = {82h:15019}, } @article {HendersonSearle81, AUTHOR = {Henderson, H. V. and Searle, S. R.}, TITLE = {On deriving the inverse of a sum of matrices}, JOURNAL = SIAMR, VOLUME = {23}, YEAR = {1981}, NUMBER = {1}, PAGES = {53--60}, MRCLASS = {15A09 (15-03 62J99)}, MRNUMBER = {82c:15005}, } @article {Herring67, AUTHOR = {Herring, G. P.}, TITLE = {A note on generalized interpolation and the pseudoinverse}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {4}, YEAR = {1967}, PAGES = {548--556}, MRCLASS = {65.20}, MRNUMBER = {36 \#2304}, } @article {Hestenes51, AUTHOR = {Hestenes, M. R.}, TITLE = {Applications of the theory of quadratic forms in {H}ilbert space to the calculus of variations}, JOURNAL = PACJM, VOLUME = {1}, YEAR = {1951}, PAGES = {525--581}, MRCLASS = {49.0X}, MRNUMBER = {13,759a}, } @article {Hestenes58, AUTHOR = {Hestenes, M. R.}, TITLE = {Inversion of matrices by biorthogonalization and related results}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {6}, YEAR = {1958}, PAGES = {51--90}, MRCLASS = {65.3X}, MRNUMBER = {19,1080d}, } @article {Hestenes61, AUTHOR = {Hestenes, M. R.}, TITLE = {Relative {H}ermitian matrices}, JOURNAL = PACJM, VOLUME = {11}, YEAR = {1961}, PAGES = {225--245}, MRCLASS = {15.30}, MRNUMBER = {25 \#1172}, } @article {Hestenes61a, AUTHOR = {Hestenes, M. R.}, TITLE = {Relative self-adjoint operators in {H}ilbert space}, JOURNAL = PACJM, VOLUME = {11}, YEAR = {1961}, PAGES = {1315--1357}, MRCLASS = {47.40}, MRNUMBER = {25 \#456}, } @article {Hestenes62, AUTHOR = {Hestenes, M. R.}, TITLE = {A ternary algelbra with applications to matrices and linear transformations}, JOURNAL = {Arch. Rational Mech. Anal.}, VOLUME = {11}, YEAR = {1962}, PAGES = {138--194}, MRCLASS = {17.10}, MRNUMBER = {27 \#169}, } @article {Hestenes73, AUTHOR = {Hestenes, M. R.}, TITLE = {On a ternary algebra}, JOURNAL = {Scripta Math.}, VOLUME = {29}, YEAR = {1973}, PAGES = {253--272}, MRCLASS = {20N10 (16A78)}, MRNUMBER = {56 \#3174}, } @article {Hestenes75, AUTHOR = {Hestenes, M. R.}, TITLE = {Pseudoinverses and conjugate gradients}, JOURNAL = COMMA1, VOLUME = {18}, YEAR = {1975}, PAGES = {40--43}, MRCLASS = {65F20}, MRNUMBER = {51 \#2269}, KEYWORDS = {comp, ginv, conjugate gradients}, } @article {HickeyLuecke82, AUTHOR = {Hickey, K. R. and Luecke, G. R.}, TITLE = {Remarks on {M}arti's method for solving first kind equations}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {19}, YEAR = {1982}, NUMBER = {3}, PAGES = {623--628}, MRCLASS = {47A50 (65J10)}, MRNUMBER = {83h:47007}, } @article {Higham86, AUTHOR = {Higham, N. J.}, TITLE = {Computing the polar decomposition---with applications}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, VOLUME = {7}, YEAR = {1986}, NUMBER = {4}, PAGES = {1160--1174}, MRCLASS = {65F25 (15A21 65F30 65F35)}, MRNUMBER = {87m:65064}, } @article{Higham87, author = {Higham, N. J.}, year = {1987}, title = {Computing Real Square Roots of a Real Matrix}, journal = {Linear Algebra and its Applications}, volume = {88/89}, pages = {405--430}, } @article{Higham88, author = {Higham, N. J.}, year = {1988}, title = {Computing a Nearest Symmetric Positive Semidefinite Matrix}, journal = {Linear Algebra and Its Applications}, volume = {103}, pages = {103-118}, } @article{HighamSchreiber90, author = {Higham, N. J. and Schreiber, R. S.}, title = {Fast Polar Decomposition of an Arbitrary Matrix}, journal = {SIAM J. Sci. Comput.}, volume = {11}, number = {4}, month = {july}, pages = {648-655}, year = {1990}, } @BOOK{Hilbert12, author = {Hilbert, D.}, title = {Grundz{\"u}ge einer algemeinen {T}heorie der linearen {I}ntegralgleichungen}, publisher = {B. G. Teubner}, year = {1912}, address = {Leipzig and Berlin}, note = {(Reprint of six articles which appeared originally in the \textit{G{\"o}tingen {N}achrichten} (1904), 49--51; (1904), 213--259; (1905), 307--338; (1906), 157--227; (1906), 439--480; (1910), 355--417)}, } @article {Hildebrandt17, AUTHOR = {Hildebrandt, T. H.}, TITLE = {On a theory of linear differential equations in {G}eneral {A}nalysis}, JOURNAL = TRAAM, VOLUME = {18}, YEAR = {1917}, PAGES = {73--96}, KEYWORDS = {General Analysis, Moore}, } @article {Hildebrandt20, AUTHOR = {Hildebrandt, T. H.}, TITLE = {On bordered {F}redholm determinants}, JOURNAL = BULAM1, VOLUME = {26}, YEAR = {1920}, PAGES = {400--405}, NOTE = {(see \cite{Dines19})}, } @article {Hilgers76, AUTHOR = {Hilgers, J. W.}, TITLE = {On the equivalence of regularization and certain reproducing kernel {H}ilbert space approaches for solving first kind problems}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {13}, YEAR = {1976}, NUMBER = {2}, PAGES = {172--184}, MRCLASS = {65J05 (65R05)}, MRNUMBER = {57 \#11030}, NOTE = {(see \cite{Hilgers78})}, } @article {Hilgers78, AUTHOR = {Hilgers, J. W.}, TITLE = {Erratum: ``{O}n the equivalence of regularization and certain reproducing kernel {H}ilbert space approaches for solving first kind problems''\ ({S}{I}{A}{M} {J}. {N}umer. {A}nal. {\bf 13} (1976), no. 2, 172--184)}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {15}, YEAR = {1978}, NUMBER = {6}, PAGES = {1301}, MRCLASS = {65R20}, MRNUMBER = {80a:65268}, } @article {Hilgers80, AUTHOR = {Hilgers, J. W.}, TITLE = {A note on estimating the optimal regularization parameter}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {17}, YEAR = {1980}, NUMBER = {3}, PAGES = {472--473}, MRCLASS = {65J10 (47A50)}, MRNUMBER = {82e:65064}, } @article {Hilgers82, AUTHOR = {Hilgers, J. W.}, TITLE = {A theory for optimal regularization in the finite-dimensional case}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {48}, YEAR = {1982}, PAGES = {359--379}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {84e:65037}, } @Article{Hodaway77, author = {Hodaway, H. W.}, title = {{GINV}, {A} Subroutine in {ANSI} Fortran for Generalized Matrix Inversion}, journal = {Australian Computer J.}, volume = {9}, number = {4}, pages = {159--161}, year = {1977}, } @ARTICLE{HoKalman66, author = {Ho, B. L. and Kalman, R. E.}, title = {Effective construction of linear state--variables models from input/output functions}, journal = {Regelungstechnik}, year = {1966}, volume = {14}, pages = {545--548}, } @article {HoKashyap66, AUTHOR = {Ho, Yu-chi and Kashyap, R. L.}, TITLE = {A class of iterative procedures for linear inequalities}, JOURNAL = {SIAM J. Control}, VOLUME = {4}, YEAR = {1966}, PAGES = {112--115}, MRCLASS = {90.50}, MRNUMBER = {33 \#3773}, } @article {HoerlKennard70, AUTHOR = {Hoerl, A. E. and Kennard, R. W.}, TITLE = {Ridge regression: {B}iased estimation of nonorthogonal problems}, JOURNAL = {Technometrics}, VOLUME = {12}, YEAR = {1970}, PAGES = {55--67}, MRCLASS = {}, MRNUMBER = {}, } @article {HoerlKennard80, AUTHOR = {Hoerl, A. E. and Kennard, R. W.}, TITLE = {A note on least squares estimates}, JOURNAL = {Communications in Statistics. Part B -- Simulation and Computations}, VOLUME = {9}, YEAR = {1980}, PAGES = {315--317}, NOTE = {(generalization of \cite{Subrahmanyan72})}, } @article {HoerlKennard81, AUTHOR = {Hoerl, A. E. and Kennard, R. W.}, TITLE = {Ridge regression---1980. {A}dvances, algorithms, and applications}, JOURNAL = {Amer. J. Math. Management Sci.}, VOLUME = {1}, YEAR = {1981}, NUMBER = {1}, PAGES = {5--83}, MRCLASS = {62J07}, MRNUMBER = {82d:62117}, } @article {Hoerl85, AUTHOR = {Hoerl, R. W.}, TITLE = {Ridge analysis 25 years later}, JOURNAL = {Amer. Statist.}, VOLUME = {39}, YEAR = {1985}, NUMBER = {3}, PAGES = {186--192}, MRCLASS = {62H99 (62J07)}, MRNUMBER = {86i:62123}, } @TECHREPORT{Holder00, AUTHOR={Holder, A.}, TITLE={Desinging Radiotherapy Plans with Elastic Constraints and Interior Point Methods}, INSTITUTION={Trinity University}, ADDRESS={San Antonio, TX}, YEAR={2000}, NUMBER={No. 49}, } @article {HolderCaron00, AUTHOR = {Holder, A. G. and Caron, R. J.}, TITLE = {Uniform bounds on the limiting and marginal derivatives of the analytic center solution over a set of normalized weights}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {26}, YEAR = {2000}, NUMBER = {2}, PAGES = {49--54}, MRCLASS = {90C51 (90C05 90C31)}, MRNUMBER = {2000j:90079}, } @TECHREPORT{HolderEtAl99, AUTHOR={Holder, A. and Sturm, J. and Zhang, S.}, TITLE={Marginal and Parametric Analysis of the Central Optimal Solution}, INSTITUTION={Trinity University Mathematics}, YEAR={1999}, NUMBER={No. 48}, NOTE={(to appear in Information Systems and Operational Research)}, } @BOOK{Holmes72, author = {Holmes, R. B.}, title = {A {C}ourse on {O}ptimization and {B}est {A}pproximation}, publisher = {Springer--Verlag}, year = {1972}, address = {Berlin}, } @PhDThesis{ Homeier96Hab, author = {H. H. H. Homeier}, title = {{Extrapolationsverfahren f\"ur Zahlen-, Vektor- und Matrizenfolgen und ihre Anwendung in der Theoretischen und Physikalischen Chemie}}, year = {1996}, type = {Habilitation thesis}, school = {Universit\"at Regensburg}, url = {http://www.chemie.uni-regensburg.de/Theoretische_Chemie/Homeier/preprint/preprint.html#Homeier96Hab}, } @InProceedings{Homeier98tvj, author = {Homeier, H. H. H.}, title = {{The vector ${\mathcal{J}}$ extrapolation method}}, booktitle = {{Iterative {M}ethods in {S}cientific {C}omputation}}, editor = { Junping Wang and Allen, {III.}, Myron B. and Chen, Benito M. and Tarek Mathew}, note = {Proceedings of the {\em Third IMACS International Symposium on Iterative Methods in Scientific Computation Jackson Hole, Wyoming, USA - July 9-12, 1997}}, year = 1998, volume = 4, pages = {375--380}, series = {IMACS Series in Computational and Applied Mathematics}, publisher = {IMACS, Dept. of Computer Science, Rutgers University, New Brunswick, NJ 08903, USA}, issn = {1098-870X}, tech = {Technical Report TC-NA-97-5, Institut f{\"u}r {P}hysikalische und {T}heoretische {C}hemie, {U}niversit{\"a}t {R}egensburg, {D}-93040 {R}egensburg, 1997}, url = {http://www.chemie.uni-regensburg.de/Theoretische_Chemie/Homeier/preprint/preprint.html#TC-NA-97-5}, } @book {HornJohnson85, AUTHOR = {Horn, R. A. and Johnson, C. R.}, TITLE = {Matrix {A}nalysis}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1985}, PAGES = {xiii+561}, ISBN = {0-521-30586-1}, MRCLASS = {15-01}, MRNUMBER = {87e:15001}, NOTE = {(corrected reprint Cambridge University Press, Cambridge, 1990)}, } @book {HornJohnson91, AUTHOR = {Horn, R. A. and Johnson, C. R.}, TITLE = {Topics in {M}atrix {A}nalysis}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1991}, PAGES = {viii+607}, ISBN = {0-521-30587-X}, MRCLASS = {15-02 (15-01 65-02)}, MRNUMBER = {92e:15003}, } @article {Hoskuldsson94, AUTHOR = {H{\"o}skuldsson, A.}, TITLE = {Data analysis, matrix decompositions, and generalized inverse}, JOURNAL = {SIAM J. Sci. Comput.}, VOLUME = {15}, YEAR = {1994}, NUMBER = {2}, PAGES = {239--262}, MRCLASS = {65F05 (15A06 15A09 15A24 65R30)}, MRNUMBER = {95a:65055}, } @article{Hotelling36, author = {Hotelling, H.}, year = {1936}, title = {Relation between two Sets of Variates}, journal = {Biometrika}, volume = {28}, pages = {322-377}, kwds = {stat, geig, gsvd, canonical correlation, multivariate analysis}, } @article{Hotelling43, author = {Hotelling, H.}, year = {1943}, title = {Some New Methods in Matrix Calculations}, journal = {Annals of Mathematical Statistics}, volume = {14}, pages = {1-34}, kwds = {stat, nla, lud}, } @article{Hotelling57, author = {Hotelling, H.}, year = {1957}, title = {Relation of the Newer Multivariate Statistical Methods to Factor Analysis}, journal = {Br. J. Static. Psychol.}, volume = {10}, pages = {69-79}, kwds = {stat, svd, principal components, factor analysis, multivariate analysis}, } @article {HoughVavasis97, AUTHOR = {Hough, P. D. and Vavasis, S. A.}, TITLE = {Complete orthogonal decomposition for weighted least squares}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {18}, YEAR = {1997}, NUMBER = {2}, PAGES = {369--392}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F05 (65F25 65G05)}, MRNUMBER = {98a:65033}, } @BOOK{Householder64, author = {Householder, A. S.}, title = {The {T}heory of {M}atrices in {N}umerical {A}nalysis}, publisher = {Blaisdell}, year = {1964}, address = {New York}, keywords = {}, } @article {Householder65, AUTHOR = {Householder, A. S.}, TITLE = {The {K}antorovich and some related inequalities}, JOURNAL = {SIAM Rev.}, VOLUME = {7}, YEAR = {1965}, PAGES = {463--473}, MRCLASS = {65.35 (65.82)}, MRNUMBER = {32 \#6656}, } @ARTICLE{HouseholderYoung38, author = {Householder, A. S. and Young, G.}, title = {Matrix approximation and latent roots}, journal = AMEMM, year = {1938}, volume = {45}, pages = {165--171}, } @article {HsuanEtAl85, AUTHOR = {Hsuan, F. C. and Langenberg, P. and Getson, A. J.}, TITLE = {The $\{2\}$-inverse with applications in statistics}, JOURNAL = LINAA1, VOLUME = {70}, YEAR = {1985}, PAGES = {241--248}, MRCLASS = {15A09}, MRNUMBER = {87b:15005}, } @Article{HuangYu97, author = {Huang, K. and Yu, J.}, title = {Remarks on a formula for the pseudoinverse by the modified {Huang} algorithm}, journal = {Computing}, volume = {59}, number = {2}, pages = {183--185}, year = {1997}, mrclass = {65F20}, mrnumber = {1 475 534}, keywords = {Algorithms; Inverse problems; Mathematical techniques; Matrix algebra; Modified Huang algorithm; Moore-Penrose pseudoinverse; Nonlinear equations}, } @article {Huang00, AUTHOR = {Huang, Liping}, TITLE = {The explicit solutions and solvability of linear matrix equations}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {311}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {195--199}, MRCLASS = {15A24}, MRNUMBER = {2000m:15019}, NOTE = {(see \cite{Brualdi00})}, } @article {HungMarkham75, AUTHOR = {Hung, C. H. and Markham, T. L.}, TITLE = {The {M}oore-{P}enrose inverse of a partitioned matrix ${M}=(\sb{{B}}\sp{{A}}$ ${}\sb{{C}}\sp{0})$}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {25(100)}, YEAR = {1975}, NUMBER = {3}, PAGES = {354--361}, MRCLASS = {15A09}, MRNUMBER = {52 \#8145}, } @article {HungMarkham77, AUTHOR = {Hung, C. H. and Markham, T. L.}, TITLE = {The {M}oore-{P}enrose inverse of a sum of matrices}, JOURNAL = {J. Austral. Math. Soc. Ser. A}, VOLUME = {24}, YEAR = {1977}, NUMBER = {4}, PAGES = {385--392}, MRCLASS = {15A09}, MRNUMBER = {58 \#715}, } @article {HurtWaid70, AUTHOR = {Hurt, M. F. and Waid, C.}, TITLE = {A generalized inverse which gives all the integral solutions to a system of linear equations}, JOURNAL = SIAJA, VOLUME = {19}, YEAR = {1970}, PAGES = {547--550}, MRCLASS = {15A06}, MRNUMBER = {45 \#1936}, } @ARTICLE{Hurwitz12, author = {Hurwitz, W. A.}, title = {On the pseudo--resolvent to the kernel of an integral equation}, journal = TRAAM, year = {1912}, volume = {13}, pages = {405--418}, keywords = {}, } @article {Huylebrouck96, AUTHOR = {Huylebrouck, D.}, TITLE = {The generalized inverse of a sum with radical element: applications}, JOURNAL = LINAA1, VOLUME = {246}, YEAR = {1996}, PAGES = {159--175}, MRCLASS = {15A09}, MRNUMBER = {97e:15003}, } @article{HuylebrouckPuystjens86, AUTHOR = {Huylebrouck, D. and Puystjens, R.}, TITLE = {Generalized inverses of a sum with a radical element}, JOURNAL = LINAA1, VOLUME = {84}, YEAR = {1986}, PAGES = {289--300}, MRCLASS = {15A09 (15A33 16A99)}, MRNUMBER = {88d:15005}, } @article {HuylebrouckEtAl84, AUTHOR = {Huylebrouck, D. and Puystjens, R. and Van Geel, J.}, TITLE = {The {M}oore-{P}enrose inverse of a matrix over a semisimple {A}rtinian ring}, JOURNAL = LINMA, VOLUME = {16}, YEAR = {1984}, NUMBER = {1-4}, PAGES = {239--246}, MRCLASS = {15A09 (15A33)}, MRNUMBER = {86g:15003}, } @article {HuylebrouckEtAl88, AUTHOR = {Huylebrouck, D. and Puystjens, R. and Van Geel, J.}, TITLE = {The {M}oore-{P}enrose inverse of a matrix over a semi-simple {A}rtinian ring with respect to an involution}, JOURNAL = LINMA, VOLUME = {23}, YEAR = {1988}, NUMBER = {3}, PAGES = {269--276}, MRCLASS = {15A09 (15A33)}, MRNUMBER = {90f:15006}, } @article {Ichim98, AUTHOR = {Ichim, I.}, TITLE = {Sur le probl\`eme des moindres carr\'es}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {326}, YEAR = {1998}, NUMBER = {5}, PAGES = {625--627}, MRCLASS = {65J10 (47A50)}, MRNUMBER = {99h:65115}, } @article {Ichim99, AUTHOR = {Ichim, I.}, TITLE = {A new solution for the least squares problem}, JOURNAL = {Int. J. Comput. Math.}, FJOURNAL = {International Journal of Computer Mathematics}, VOLUME = {72}, YEAR = {1999}, NUMBER = {2}, PAGES = {207--222}, MRCLASS = {65J10 (65F20)}, MRNUMBER = {2000h:65075}, } @incollection {IdrissiEtAl89, AUTHOR = {Idrissi, H. and Lefebvre, O. and Michelot, C.}, TITLE = {Applications and numerical convergence of the partial inverse method}, BOOKTITLE = {Optimization ({V}aretz, 1988)}, PAGES = {39--54}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1989}, MRCLASS = {90C20 (65K05 90B05 90B10)}, MRNUMBER = {91f:90098}, } @ARTICLE{Ijiri65, author = {Ijiri, Y.}, title = {On the generalized inverse of an incidence matrix}, journal = {J. Soc. Indust. Appl. Math.}, year = {1965}, volume = {13}, pages = {941--945}, keywords = {}, } @article {IkramovHD74, AUTHOR = {Ikramov, Kh. D.}, TITLE = {The eigenvalues of a pseudoinverse matrix}, JOURNAL = {Vestnik Moskov. Univ. Ser. I Mat. Meh.}, VOLUME = {29}, YEAR = {1974}, NUMBER = {3}, PAGES = {5--8}, MRCLASS = {15A09}, MRNUMBER = {50 \#2195}, } @article {Ikramov99, AUTHOR = {Ikramov, Kh. D.}, TITLE = {An algebraic proof of a result by {G}onzaga and {L}ara}, JOURNAL = LINAA1, VOLUME = {299}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {191--194}, MRCLASS = {15A12}, MRNUMBER = {2000h:15009}, } @article {Ipsen00, AUTHOR = {Ipsen, I. C. F.}, TITLE = {An overview of relative $\sin\Theta$ theorems for invariant subspaces of complex matrices}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {123}, YEAR = {2000}, NUMBER = {1-2}, PAGES = {131--153}, MRCLASS = {65F15 (65F35)}, MRNUMBER = {1 798 523}, } @article {Ipsen00a, AUTHOR = {Ipsen, I. C. F.}, TITLE = {Absolute and relative perturbation bounds for invariant subspaces of matrices}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {309}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {45--56}, MRCLASS = {15A18 (65F35)}, MRNUMBER = {1 758 360}, } @article {IpsenMeyer95, AUTHOR = {Ipsen, I. C. F. and Meyer, Jr., C. D.}, TITLE = {The angle between complementary subspaces}, JOURNAL = AMEMM, VOLUME = {102}, YEAR = {1995}, NUMBER = {10}, PAGES = {904--911}, MRCLASS = {15A03}, MRNUMBER = {96j:15002}, } @article {IpsenMeyer98, AUTHOR = {Ipsen, I. C. F. and Meyer, Jr., C. D.}, TITLE = {The idea behind {K}rylov methods}, JOURNAL = AMEMM, VOLUME = {105}, YEAR = {1998}, NUMBER = {10}, PAGES = {889--899}, MRCLASS = {65F10}, MRNUMBER = {99g:65040}, } @incollection {ItikiEtAl95, AUTHOR = {Itiki, C. and Kalaba, R. E. and Udwadia, F. E.}, TITLE = {Appell's equations of motion and the generalized inverse form}, BOOKTITLE = {Recent {T}rends in {O}ptimization {T}heory and {A}pplications}, PAGES = {123--143}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1995}, MRCLASS = {70F25}, MRNUMBER = {96k:70015}, } @preamble{ "\def\cprime{$'$} " } @article {IvanovKudrinskii66, AUTHOR = {Ivanov, V. V. and Kudrinskii, V. Yu.}, TITLE = {Approximate solution of linear operator equations in {H}ilbert space by the method of least squares. {I}}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {6}, YEAR = {1966}, NUMBER = {5}, PAGES = {831--841}, MRCLASS = {}, MRNUMBER = {}, } @article {Izumino83, AUTHOR = {Izumino, Saichi}, TITLE = {Convergence of generalized inverses and spline projectors}, JOURNAL = {J. Approx. Theory}, VOLUME = {38}, YEAR = {1983}, NUMBER = {3}, PAGES = {269--278}, MRCLASS = {41A65 (47A99)}, MRNUMBER = {85c:41054}, } @incollection {Jackson78, AUTHOR = {Jackson, D. D.}, TITLE = {Linear inverse theory with a priori data}, BOOKTITLE = {Applied inverse problems}, PAGES = {83--102}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1978}, MRCLASS = {}, MRNUMBER = {81f:65033}, } @article {Jacobi1841a, AUTHOR = {Jacobi, C. G. J.}, TITLE = {De formatione et proprietatibus Determinantium}, JOURNAL = {Crelle Journal f\"{u}r die reine und angewandte Mathematik}, VOLUME = {22}, YEAR = {1841}, PAGES = {285--318}, NOTE = {(reprinted in \textit{C.G.J. Jacobi's Gesammelte Werke} (K. Weierstrass, editor), Vol. 3, 355--392, Berlin 1884)}, } @article {Jacobi1841, AUTHOR = {Jacobi, C. G. J.}, TITLE = {De Determinantibus Functionalibus}, JOURNAL = {Crelle Journal f\"{u}r die reine und angewandte Mathematik}, VOLUME = {22}, YEAR = {1841}, PAGES = {319--359}, NOTE = {(reprinted in \textit{C.G.J. Jacobi's Gesammelte Werke} (K. Weierstrass, editor), Vol. 3, 393--438, Berlin 1884)}, } @article {Jacobson39, AUTHOR = {Jacobson, N.}, TITLE = {An application of {E}. {H}. {M}oore's determinant of a {H}ermitian matrix}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {45}, YEAR = {1939}, PAGES = {745--748}, MRCLASS = {15.0X}, MRNUMBER = {1,35c}, } @article {Jain82, AUTHOR = {Jain, S. K.}, TITLE = {Nonnegative rectangular matrices having certain nonnegative ${W}$-weighted group inverses}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {85}, YEAR = {1982}, NUMBER = {1}, PAGES = {1--9}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {84h:15004}, } @article {JainEtAl96, AUTHOR = {Jain, S. K. and Mitra, S. K. and Werner, H. {-J}.}, TITLE = {Extensions of $\mathcal{G}$-based matrix partial orders}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {17}, YEAR = {1996}, NUMBER = {4}, PAGES = {834--850}, MRCLASS = {15A30}, MRNUMBER = {97g:15017}, } @article{James92, author = {James, D.}, year = {1992}, title = {Implicit Nullspace Iterative Methods for Constrained Least Squares Problems}, journal = {SIAM J. Matrix. Anal. Appl.}, volume = {13}, pages = {962--978}, kwds = {nla, lsq, constraints, sparse}, } @article {JammalamadakaSengupta99, AUTHOR = {Jammalamadaka, S. R. and Sengupta, D.}, TITLE = {Changes in the general linear model: a unified approach}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {225--242}, MRCLASS = {62J12}, MRNUMBER = {2000a:62167}, } @article {JanakiramanRenganathan82, AUTHOR = {Janakiraman, P. A. and Renganathan, S.}, TITLE = {Recursive computation of pseudo-inverse of matrices}, JOURNAL = {Automatica---J. IFAC}, FJOURNAL = {Automatica. The Journal of IFAC. The International Federation of Automatic Control}, VOLUME = {18}, YEAR = {1982}, NUMBER = {5}, PAGES = {631--633}, MRCLASS = {65F20}, MRNUMBER = {84c:65067}, } @article {Jarnicki87, AUTHOR = {Jarnicki, M.}, TITLE = {A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of $\delta$-tempered functions}, JOURNAL = {Dissertationes Math. (Rozprawy Mat.)}, VOLUME = {258}, YEAR = {1987}, PAGES = {50}, MRCLASS = {32D15 (32E25)}, MRNUMBER = {89g:32022}, } @article {Jensen94, AUTHOR = {Jensen, D. R.}, TITLE = {Minimal properties of {M}oore-{P}enrose inverses}, JOURNAL = LINAA1, VOLUME = {196}, YEAR = {1994}, PAGES = {175--182}, MRCLASS = {15A09}, MRNUMBER = {95c:15009}, KEYWORDS = {matord, invMP}, } @article {JeromeSchumaker68, AUTHOR = {Jerome, J. W. and Schumaker, L. L.}, TITLE = {A note on obtaining natural spline functions by the abstract approach of {A}tteia and {L}aurent}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {5}, YEAR = {1968}, PAGES = {657--663}, MRCLASS = {41.30}, MRNUMBER = {40 \#6127}, } @article {JeterPye81, AUTHOR = {Jeter, M. W. and Pye, W. C.}, TITLE = {A note on nonnegative rank factorizations}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {38}, YEAR = {1981}, PAGES = {171--173}, MRCLASS = {15A23 (15A48)}, MRNUMBER = {82m:15017}, } @article {Ji89, AUTHOR = {Ji, J.}, TITLE = {The algebraic perturbation method for generalized inverses}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications}, VOLUME = {7}, YEAR = {1989}, NUMBER = {4}, PAGES = {327--333}, MRCLASS = {65F05 (65F20)}, MRNUMBER = {1 149 701}, } @article {Ji94, AUTHOR = {Ji, J.}, TITLE = {An alternative limit expression of {D}razin inverse and its application}, JOURNAL = {Appl. Math. Comput.}, VOLUME = {61}, YEAR = {1994}, NUMBER = {2-3}, PAGES = {151--156}, MRCLASS = {15A09}, MRNUMBER = {95b:15005}, } @article {JiangBerry00, AUTHOR = {Jiang, E. P. and Berry, M. W.}, TITLE = {Solving total least-squares problems in information retrieval}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {316}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {137--156}, MRCLASS = {65F20 (15A18 68P20)}, MRNUMBER = {2001e:65068}, KEYWORDS = {Generalized SVD} } @article {Jiang96, AUTHOR = {Jiang, Sheng}, TITLE = {Angles between {E}uclidean subspaces}, JOURNAL = {Geom. Dedicata}, FJOURNAL = {Geometriae Dedicata}, VOLUME = {63}, YEAR = {1996}, NUMBER = {2}, PAGES = {113--121}, MRCLASS = {51M05 (51M16)}, MRNUMBER = {97h:51020}, } @inproceedings {JodarEtAl91, AUTHOR = {J{\'o}dar, L. and Law, A. G. and Rezazadeh, A. and Weston, J. H. and Wu, G.}, TITLE = {Computations for the {M}oore {P}enrose and other generalized inverses}, BOOKTITLE = {Proceedings of the {T}wentieth {M}anitoba {C}onference on {N}umerical {M}athematics and {C}omputing ({W}innipeg, {MB}, 1990)}, JOURNAL = {Congr. Numer.}, FJOURNAL = {Congressus Numerantium}, VOLUME = {80}, YEAR = {1991}, PAGES = {57--64}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {92f:65050}, } @ARTICLE{JohnJA70, author = {John, J. A.}, title = {Use of generalized inverse matrices in {MANOVA}}, journal = {J. Roy. Statist. Soc. Ser. B}, year = {1970}, volume = {32}, pages = {137--143}, } @ARTICLE{JohnPWM64, author = {John, P. W. M.}, title = {Pseudo--inverses in the analysis of variance}, journal = {Ann. Math. Statist.}, year = {1964}, volume = {35}, pages = {895--896}, } @article {JohnsonEtAl94, AUTHOR = {Johnson, C. R. and Kerr, M. K. and Stanford, D. P.}, TITLE = {Semipositivity of matrices}, JOURNAL = LINMA, VOLUME = {37}, YEAR = {1994}, NUMBER = {4}, PAGES = {265--271}, MRCLASS = {15A48 (15A09)}, MRNUMBER = {95m:15032}, NOTE = {(see \cite{Werner94a})}, } @article{JohnsonEtAl96, AUTHOR = {Johnson, C. R. and Loewy, R. and Olesky, D. D. and van den Driessche, P.}, TITLE = {Maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices}, JOURNAL = LINAA1, VOLUME = {241/243}, YEAR = {1996}, PAGES = {635--654}, MRCLASS = {15A48 (15A18)}, MRNUMBER = {97f:15040}, } @article {JonesEtAl98, AUTHOR = {Jones, Jon and Karampetakis, N. P. and Pugh, A. C.}, TITLE = {The computation and application of the generalized inverse via {M}aple}, JOURNAL = {J. Symbolic Comput.}, FJOURNAL = {Journal of Symbolic Computation}, VOLUME = {25}, YEAR = {1998}, NUMBER = {1}, PAGES = {99--124}, ISSN = {0747-7171}, MRCLASS = {65-04 (65F10)}, MRNUMBER = {1 600 622}, } @ARTICLE{Jones65, author = {Jones, Jr., J.}, title = {On the {L}yapunov stability criteria}, journal = {J. Soc. Indust. Appl. Math.}, year = {1965}, volume = {13}, pages = {941--945}, } @ARTICLE{Jones72, author = {Jones, Jr., J.}, title = {Solution of certain matrix equations}, journal = PROAM, year = {1972}, volume = {31}, pages = {333--339}, } @article {Jongmans60, AUTHOR = {Jongmans, F.}, TITLE = {Resolution num\'erique de l'\'equation matricielle ${A}{X}{B}={C}$}, JOURNAL = {Simon Stevin}, VOLUME = {34}, YEAR = {1960/1961}, PAGES = {3--26}, MRCLASS = {65.35}, MRNUMBER = {23 \#B2578}, } @incollection {Jongmans68, AUTHOR = {Jongmans, F.}, TITLE = {Retour critique sur l'\'equation matricielle ${A}{X}{B}={C}$}, BOOKTITLE = {Hommage au {P}rofesseur {L}ucien {G}odeaux}, PAGES = {127--134}, PUBLISHER = {Librairie Universitaire, Louvain}, YEAR = {1968}, MRCLASS = {15.35}, MRNUMBER = {39 \#1471}, } @article {Jordan1874, AUTHOR = {Jordan, C.}, TITLE = {M{\'e}moires sur les formes bilin{\'e}aires}, JOURNAL = {J. Math. Pures Appl. Deuxi{\`e}me S{\'e}r.}, VOLUME = {19}, YEAR = {1874}, PAGES = {35--54}, NOTE = {(see history of SVD in \cite{Stewart93})}, KEYWORDS = {SVD}, } @article {Jordan1874a, AUTHOR = {Jordan, C.}, TITLE = {Sur la r{\'e}duction des formes bilin{\'e}aires}, JOURNAL = {C. R. de l'Acad. Sci. Paris}, VOLUME = {78}, YEAR = {1874}, PAGES = {614--617}, NOTE = {(see history of SVD in \cite{Stewart93})}, KEYWORDS = {SVD}, } @article {Jordan1875, AUTHOR = {Jordan, C.}, TITLE = {Essai sur la g{\'e}ometry \`a n dimensions}, JOURNAL = {Bull. Soc. Math.}, VOLUME = {3}, YEAR = {1874}, PAGES = {103--174}, NOTE = {(see history of angles in \cite[p. 45]{StewartSun90})}, KEYWORDS = {Geometry}, } @article {Joshi73, AUTHOR = {Joshi, V. N.}, TITLE = {Remarks on iterative methods for computing the generalised inverse}, JOURNAL = {Studia Sci. Math. Hungar.}, VOLUME = {8}, YEAR = {1973}, PAGES = {457--461}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {50 \#6133}, } @article {Joshi80, AUTHOR = {Joshi, V. N.}, TITLE = {A determinant for rectangular matrices}, JOURNAL = {Bull. Austral. Math. Soc.}, VOLUME = {21}, YEAR = {1980}, NUMBER = {1}, PAGES = {137--146}, MRCLASS = {15A15 (15A09)}, MRNUMBER = {81k:15005}, } @article {JoshiTewarson72, AUTHOR = {Joshi, V. N. and Tewarson, R. P.}, TITLE = {On solving ill-conditioned systems of linear equations}, JOURNAL = {Trans. New York Acad. Sci. (2)}, VOLUME = {34}, YEAR = {1972}, PAGES = {565--571}, MRCLASS = {15A12}, MRNUMBER = {51 \#12882}, } @article {Kabe85, AUTHOR = {Kabe, D. G.}, TITLE = {On unified singular least squares theory}, JOURNAL = {Indust. Math.}, FJOURNAL = {Industrial Mathematics}, VOLUME = {35}, YEAR = {1985}, NUMBER = {2}, PAGES = {97--104}, MRCLASS = {62J05}, MRNUMBER = {88e:62164}, } @article {Kaczmarz37, AUTHOR = {Kaczmarz, S.}, TITLE = {Angen{\"a}herte {A}ufl{\"o}sung von {S}ystemen linearer {G}leichungen}, JOURNAL = {Bulletin de l'Acad{\'e}mie Polonaise des Sciences et Lettres}, VOLUME = {A35}, YEAR = {1937}, PAGES = {355--357}, } @article {Kaffes81, AUTHOR = {Kaffes, D. G.}, TITLE = {An inequality for matrices}, JOURNAL = {Bull. Soc. Math. Gr\`ece (N.S.)}, FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de Gr\`ece. Nouvelle S\'erie}, VOLUME = {22}, YEAR = {1981}, PAGES = {143--159}, MRCLASS = {15A45 (15A09 15A48)}, MRNUMBER = {87e:15039}, } @article {KaffesEtAl89, AUTHOR = {Kaffes, D. G. and Mathew, T. and Rao, M. Bhaskara and Subramanyam, K.}, TITLE = {On the matrix convexity of the {M}oore-{P}enrose inverse and some applications}, JOURNAL = LINMA, VOLUME = {24}, YEAR = {1989}, NUMBER = {4}, PAGES = {265--271}, MRCLASS = {15A09 (15A52)}, MRNUMBER = {90j:15010}, } @book {Kahan01, AUTHOR = {Kahan, W.}, TITLE = {Huge generalized inverses of rank--defficient matrices}, PUBLISHER = {University of Calfornia at Berkley}, YEAR = {2001}, NOTE = {(online lecture notes)}, URL = {http://www.cs.berkeley.edu/~wkahan/MathH110/gilite.pdf}, } @article {Kala81, AUTHOR = {Kala, R.}, TITLE = {Projectors and linear estimation in general linear models}, JOURNAL = {Comm. Statist. A---Theory Methods}, FJOURNAL = {Communications in Statistics. A. Theory and Methods}, VOLUME = {10}, YEAR = {1981}, NUMBER = {9}, PAGES = {849--873}, MRCLASS = {62J05}, MRNUMBER = {83c:62108}, } @article {KalabaUdwadia92, AUTHOR = {Kalaba, R. E. and Udwadia, F. E.}, TITLE = {On constrained motion}, JOURNAL = APPMC, VOLUME = {51}, YEAR = {1992}, NUMBER = {1}, PAGES = {85--86}, MRCLASS = {70F99 (70H30)}, MRNUMBER = {93i:70014}, KEYWORDS = {appdif, appcon}, } @article {KalabaUdwadia94, AUTHOR = {Kalaba, R. E. and Udwadia, F. E.}, TITLE = {Lagrangian mechanics, {G}auss' principle, quadratic programming, and generalized inverses: new equations for non-holonomically constrained discrete mechanical systems}, JOURNAL = QUAAM, VOLUME = {52}, YEAR = {1994}, NUMBER = {2}, PAGES = {229--241}, MRCLASS = {70F25 (70H30 90C90)}, MRNUMBER = {95c:70019}, } @article {KalabaEtAl95, AUTHOR = {Kalaba, R. E. and Udwadia, F. E. and Xu, R.}, TITLE = {Constrained motion revisited}, JOURNAL = APPMC, VOLUME = {70}, YEAR = {1995}, NUMBER = {1}, PAGES = {67--76}, MRCLASS = {70F25 (49S05 70H30)}, MRNUMBER = {95m:70004}, } @article {KalabaEtAl95a, AUTHOR = {Kalaba, R. E. and Udwadia, F. E. and Xu, R. and Itiki, C.}, TITLE = {The equivalence of {L}agrange's equations of motion of the first kind and the generalized inverse form}, JOURNAL = {Nonlinear World}, VOLUME = {2}, YEAR = {1995}, NUMBER = {4}, PAGES = {519--526}, MRCLASS = {70H35}, MRNUMBER = {96k:70033}, } @article {KalabaXu95, AUTHOR = {Kalaba, R. E. and Xu, Rong}, TITLE = {On the generalized inverse form of the equations of constrained motion}, JOURNAL = {Amer. Math. Monthly}, VOLUME = {102}, YEAR = {1995}, NUMBER = {9}, PAGES = {821--825}, MRCLASS = {70F99 (15A09 70H30)}, MRNUMBER = {96h:70018}, } @ARTICLE{Kakutani39, author = {Kakutani, S.}, title = {Some characterizations of {E}uclidean spaces}, journal = {Japan J. Math.}, year = {1939}, volume = {16}, pages = {93--97}, } @ARTICLE{Kallina69, author = {Kallina, C.}, title = {A {G}reen's function approach to perturbations of periodic solutions}, journal = PACJM, year = {1969}, volume = {29}, pages = {325--334}, } @ARTICLE{Kalman60, author = {Kalman, R. E.}, title = {Contributions to the theory of optimal control}, journal = {Bol. Soc. Mat. Mexicana}, year = {1960}, volume = {5}, number = {2}, pages = {102--119}, } @ARTICLE{Kalman60a, author = {Kalman, R. E.}, title = {A new approach to linear filtering and prediction problems}, journal = {Trans. ASME Ser. D. J. Basic Eng.}, year = {1960}, volume = {82}, pages = {35--45}, } @ARTICLE{Kalman61, author = {Kalman, R. E.}, title = {New results in linear filtering and prediction problems}, journal = {Trans. ASME Ser. D. J. Basic Eng.}, year = {1961}, volume = {83}, pages = {95--107}, } @ARTICLE{Kalman63, author = {Kalman, R. E.}, title = {Mathematical description of linear dynamical systems}, journal = {SIAM J. Control}, year = {1963}, volume = {1}, pages = {152--192}, } @incollection {Kalman76, AUTHOR = {Kalman, R. E.}, TITLE = {Algebraic aspects of the generalized inverses of a rectangular matrix}, BOOKTITLE = {Generalized {I}nverses and {A}pplications ({P}roc. {S}em., {M}ath. {R}es. {C}enter, {U}niv. {W}isconsin, {M}adison, {W}is., 1973)}, editor = {Nashed, M. Z.}, publisher = {Academic Press}, address = {New York}, PAGES = {189--213}, YEAR = {1976}, } @incollection {KalmanEtAl63, AUTHOR = {Kalman, R. E. and Ho, Y. C. and Narendra, K. S.}, TITLE = {Controllability of linear dynamical systems}, BOOKTITLE = {Contributions to {D}ifferential {E}quations, {V}ol. {I}}, PAGES = {189--213}, PUBLISHER = {Interscience}, ADDRESS = {New York}, YEAR = {1963}, } @article {Kaltenbacher97, AUTHOR = {Kaltenbacher, B.}, TITLE = {Some {N}ewton-type methods for the regularization of nonlinear ill-posed problems}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {13}, YEAR = {1997}, NUMBER = {3}, PAGES = {729--753}, MRCLASS = {65J20}, MRNUMBER = {98h:65025}, } @article {KammererNashed71, AUTHOR = {Kammerer, W. J. and Nashed, M. Z.}, TITLE = {Steepest descent for singular linear operators with nonclosed range}, JOURNAL = {Applicable Anal.}, VOLUME = {1}, YEAR = {1971}, NUMBER = {2}, PAGES = {143--159}, MRCLASS = {47.10 (65.00)}, MRNUMBER = {44 \#7319}, } @article {KammererNashed71a, AUTHOR = {Kammerer, W. J. and Nashed, M. Z.}, TITLE = {A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {51}, YEAR = {1971}, PAGES = {20--25}, } @article {KammererNashed72, AUTHOR = {Kammerer, W. J. and Nashed, M. Z.}, TITLE = {Iterative methods for best approximate solutions of linear integral equations of the first and second kinds}, JOURNAL = JMATA, VOLUME = {40}, YEAR = {1972}, PAGES = {547--573}, } @article {KammererNashed72a, AUTHOR = {Kammerer, W. J. and Nashed, M. Z.}, TITLE = {On the convergence of the conjugate gradient method for singular linear operator equations}, JOURNAL = SIAJN, VOLUME = {9}, YEAR = {1972}, PAGES = {165--181}, } @BOOK{KantorovichAkilov64, author = {Kantorovich, L. V. and Akilov, G. P.}, title = {Functional {A}nalysis in {N}ormed {S}paces}, publisher = {Pergamon Press}, year = {1964}, address = {Oxford}, note = {(translated from Russian)}, } @BOOK{KantorovichKrylov58, author = {Kantorovich, L. V. and Krylov, V. I.}, title = {Approximate {M}ethods of {H}igher {A}nalysis}, publisher = {Interscience}, year = {1958}, address = {New York}, note = {(translated from Russian)}, } @article {Karampetakis97, AUTHOR = {Karampetakis, N. P.}, TITLE = {Computation of the generalized inverse of a polynomial matrix and applications}, JOURNAL = LINAA1, VOLUME = {252}, YEAR = {1997}, PAGES = {35--60}, MRCLASS = {65F20 (93C05)}, MRNUMBER = {98c:65066}, } @article {Karampetakis97a, AUTHOR = {Karampetakis, N. P.}, TITLE = {Generalized inverses of two-variable polynomial matrices and applications}, JOURNAL = {Circuits Systems Signal Process.}, FJOURNAL = {Circuits, Systems, and Signal Processing}, VOLUME = {16}, YEAR = {1997}, NUMBER = {4}, PAGES = {439--453}, MRCLASS = {15A09 (39B42 65F20 93C35)}, MRNUMBER = {98i:15008}, } @article {Karasalo74, AUTHOR = {Karasalo, I.}, TITLE = {A criterion for truncation of the ${Q}{R}$-decomposition algorithm for the singular linear least squares problem}, JOURNAL = {Nordisk Tidskr. Informationsbehandling (BIT)}, VOLUME = {14}, YEAR = {1974}, PAGES = {156--166}, MRCLASS = {65F20}, MRNUMBER = {58 \#3372}, } @article {Kass89, AUTHOR = {Kass, S.}, TITLE = {Spaces of closest fit}, JOURNAL = LINAA1, VOLUME = {117}, YEAR = {1989}, PAGES = {93--97}, MRCLASS = {51K05 (15A03 15A99)}, MRNUMBER = {90f:51018}, } @article {KatoMoriya77, AUTHOR = {Kato, Yoshinobu and Moriya, Nobuhiro}, TITLE = {Maeda's inequality for pseudoinverses}, JOURNAL = {Math. Japon.}, VOLUME = {22}, YEAR = {1977}, NUMBER = {1}, PAGES = {89--91}, MRCLASS = {47A30}, MRNUMBER = {56 \#6434}, MRREVIEWER = {Chandler Davis}, } @article {KatsaggelosEfstratiadis90, AUTHOR = {Katsaggelos, A. K. and Efstratiadis, S. N.}, TITLE = {A class of iterative signal restoration algorithms}, JOURNAL = {IEEE Trans. Acoust. Speech Signal Process.}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Acoustics, Speech, and Signal Processing}, VOLUME = {38}, YEAR = {1990}, NUMBER = {5}, PAGES = {778--786}, MRCLASS = {94A12 (65F05)}, MRNUMBER = {91f:94006}, KEYWORDS = {appvis}, } @ARTICLE{Katz65, author = {Katz, I. J.}, title = {Wiegmann type theorems for {$EP_r$} matrices}, journal = {Duke Math. J.}, year = {1965}, volume = {32}, pages = {423--427}, } @article {Katz70, AUTHOR = {Katz, I. J.}, TITLE = {Remarks on a paper of {B}en-{I}srael}, JOURNAL = SIAJA, VOLUME = {18}, YEAR = {1970}, PAGES = {511--513}, MRCLASS = {15.10}, MRNUMBER = {41 \#6863}, } @article {KatzPearl66, AUTHOR = {Katz, I. J. and Pearl, M. H.}, TITLE = {On ${E}{P}r$ and normal ${E}{P}r$ matrices}, JOURNAL = {J. Res. Nat. Bur. Standards Sect. B}, VOLUME = {70B}, YEAR = {1966}, PAGES = {47--77}, MRCLASS = {15.30}, MRNUMBER = {33 \#7358}, KEYWORDS = {matEP}, } @article {KatzPearl66a, AUTHOR = {Katz, I. J. and Pearl, M. H.}, TITLE = {Solutions of the matrix equation ${A}\sp{\ast} ={X}{A}={A}{X}$}, JOURNAL = {J. London Math. Soc.}, VOLUME = {41}, YEAR = {1966}, PAGES = {443--452}, MRCLASS = {15.35}, MRNUMBER = {33 \#4072}, } @article {KaufmanPereyra78, AUTHOR = {Kaufman, L. and Pereyra, V.}, TITLE = {A method for separable nonlinear least squares problems with separable nonlinear equality constraints}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {15}, YEAR = {1978}, NUMBER = {1}, PAGES = {12--20}, MRCLASS = {90C30}, MRNUMBER = {57 \#11766}, KEYWORS = {Nonlinear least squares}, } @article{Keller65, author = {H. B. Keller}, year = {1965}, title = {On the Solution of Singular and Semidefinite Linear Systems by Iteration}, journal = {SIAM Journal on Numerical Analysis}, volume = {2}, pages = {281--290}, kwds = {nla, linear system, iter, singular system}, } @article {Keller-McNultyKennedy87, AUTHOR = {Keller-McNulty, S. and Kennedy, W. J.}, TITLE = {Error-free computation of the {M}oore-{P}enrose inverse with application to linear least squares analysis}, JOURNAL = {J. Statist. Comput. Simulation}, VOLUME = {27}, YEAR = {1987}, NUMBER = {1}, PAGES = {45--64}, MRCLASS = {65F20 (65D10 65U05)}, MRNUMBER = {90a:65093}, } @article {Kelly98, AUTHOR = {Kelly, J. D.}, TITLE = {A regularization approach to the reconciliation of constrained data sets}, JOURNAL = {Computers \& Chemical Engineering}, VOLUME = {22}, YEAR = {1998}, PAGES = {1771--1788}, } @article {Khabaza63, AUTHOR = {Khabaza, I. M.}, TITLE = {An iterative least-square method suitable for solving large sparse matrices}, JOURNAL = {Comput. J.}, VOLUME = {6}, YEAR = {1963/1964}, PAGES = {202--206}, MRCLASS = {65.35}, MRNUMBER = {27 \#4351}, } @incollection {KhajdukovEtAl97, AUTHOR = {Khajdukov, V. G. and Kostin, V. I. and Tcheverda, V. A.}, TITLE = {The $r$-solution and its applications in linearized waveform inversion for a layered background}, BOOKTITLE = {Inverse {P}roblems in {W}ave {P}ropagation ({M}inneapolis, {MN}, 1995)}, PAGES = {277--294}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1997}, MRCLASS = {35R30 (35L05 65M12 76Q05)}, MRNUMBER = {98j:35185}, } @article {Khatri67, AUTHOR = {Khatri, C. G.}, TITLE = {A theorem on least squares in multivariate linear regression}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {62}, YEAR = {1967}, PAGES = {1494--1495}, MRCLASS = {}, MRNUMBER = {36 \#3464}, } @article {Khatri69, AUTHOR = {Khatri, C. G.}, TITLE = {A note on some results on a generalised inverse of a matrix}, JOURNAL = {J. Indian Statist. Assoc.}, VOLUME = {7}, YEAR = {1969}, PAGES = {38--45}, MRCLASS = {}, MRNUMBER = {48 \#3980}, } @article {Khatri70, AUTHOR = {Khatri, C. G.}, TITLE = {A note on a commutative $g$-inverse of a matrix}, JOURNAL = {Sankhy\=a Ser. A}, VOLUME = {32}, YEAR = {1970}, PAGES = {299--310}, MRCLASS = {15A09}, MRNUMBER = {45 \#1939}, } @article {Khatri82, AUTHOR = {Khatri, C. G.}, TITLE = {A representation of a matrix and its use in the {G}auss-{M}arkoff model}, JOURNAL = {J. Indian Statist. Assoc.}, VOLUME = {20}, YEAR = {1982}, PAGES = {89--98}, MRCLASS = {62J05 (62F10)}, MRNUMBER = {86k:62115}, } @article {Khatri83, AUTHOR = {Khatri, C. G.}, TITLE = {A generalization of {L}avoie's inequality concerning the sum of idempotent matrices}, JOURNAL = LINAA1, VOLUME = {54}, YEAR = {1983}, PAGES = {97--108}, MRCLASS = {15A09 (15A18)}, MRNUMBER = {85i:15006}, } @article {Khatri85, AUTHOR = {Khatri, C. G.}, TITLE = {A note on idempotent matrices}, JOURNAL = LINAA1, VOLUME = {70}, YEAR = {1985}, PAGES = {185--195}, MRCLASS = {15A57 (15A09)}, MRNUMBER = {87d:15019}, } @article {Khatri85a, AUTHOR = {Khatri, C. G.}, TITLE = {Commutative $g$-inverse of a matrix}, JOURNAL = {Math. Today}, FJOURNAL = {Mathematics Today}, VOLUME = {3}, YEAR = {1985}, PAGES = {37--40}, MRCLASS = {15A09}, MRNUMBER = {87b:15006}, } @article {Khatri89, AUTHOR = {Khatri, C. G.}, TITLE = {Study of redundancy of vector variables in canonical correlations}, JOURNAL = {Comm. Statist. Theory Methods}, FJOURNAL = {Communications in Statistics. Theory and Methods}, VOLUME = {18}, YEAR = {1989}, NUMBER = {4}, PAGES = {1425--1440}, MRCLASS = {62H20}, MRNUMBER = {91b:62114}, } @article {KhatriMitra76, AUTHOR = {Khatri, C. G. and Mitra, S. K.}, TITLE = {Hermitian and nonnegative solutions of linear matrix equations}, JOURNAL = SIAJA, VOLUME = {31}, YEAR = {1976}, PAGES = {579--585}, } @article {KhatriRao81, AUTHOR = {Khatri, C. G. and Rao, C. R.}, TITLE = {Some extensions of the {K}antorovich inequality and statistical applications}, JOURNAL = {J. Multivariate Anal.}, VOLUME = {11}, YEAR = {1981}, NUMBER = {4}, PAGES = {498--505}, MRCLASS = {15A15 (15A45 62J05)}, MRNUMBER = {84e:15006}, } @incollection {Kiekebusch-Muller77, AUTHOR = {Kiekebusch-M{\"u}ller, B. D.}, TITLE = {A class of algorithms for the determination of a solution of a system of nonlinear equations}, BOOKTITLE = {Optimization {T}echniques ({P}roc. 8th {IFIP} {C}onf., {W}{\"u}rzburg, 1977), {P}art 2}, PAGES = {67--75. Lecture Notes in Control and Informat. Sci., Vol. 7}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1978}, MRCLASS = {65H10}, MRNUMBER = {58 \#13678}, } @article {KimLee86, AUTHOR = {Kim, Byung Chun and Lee, Jang Taek}, TITLE = {The {M}oore-{P}enrose inverse for the classificatory models}, JOURNAL = {J. Korean Statist. Soc.}, VOLUME = {15}, YEAR = {1986}, NUMBER = {1}, PAGES = {46--61}, MRCLASS = {15A09 (15A06 62J10)}, MRNUMBER = {87m:15012}, } @article {KimOh99, AUTHOR = {Kim, Doh-Hyun and Oh, Jun-Ho}, TITLE = {The {M}oore-{P}enrose inverse for the classificatory models}, JOURNAL = {Control Engineering Practice}, VOLUME = {7}, YEAR = {1999}, NUMBER = {3}, PAGES = {369--373}, } @article {KimS98, AUTHOR = {Kim, S.}, TITLE = {Generalized inverses in numerical solutions of {C}auchy singular integral equations}, JOURNAL = {Commun. Korean Math. Soc.}, VOLUME = {13}, YEAR = {1998}, NUMBER = {4}, PAGES = {875--888}, MRCLASS = {65R32}, MRNUMBER = {2000i:65223}, } @article {KimS98a, AUTHOR = {Kim, S.}, TITLE = {Solving singular integral equations using {G}aussian quadrature and overdetermined system}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {35}, YEAR = {1998}, NUMBER = {10}, PAGES = {63--71}, MRCLASS = {65R20 (65D32)}, MRNUMBER = {99b:65175}, } @article {KimS99, AUTHOR = {Kim, S.}, TITLE = {Numerical Solutions of Cauchy Singular Integral Equations Using Generalized Inverses}, JOURNAL = {Computers \& Mathematics with Applications}, VOLUME = {38}, YEAR = {1999}, NUMBER = {5--6}, PAGES = {183--195}, } @article {King77, AUTHOR = {King, Chen F.}, TITLE = {A note on {D}razin inverses}, JOURNAL = {Pacific J. Math.}, VOLUME = {70}, YEAR = {1977}, NUMBER = {2}, PAGES = {383--390}, MRCLASS = {47B30 (47A05)}, MRNUMBER = {58 \#2418}, } @PHDTHESIS{Kirby65, author = {Kirby, M. J. L.}, title = {Generalized {I}nverses and {C}hance {C}onstrained {P}rogramming}, school = {Northwestern Univ.}, year = {1965}, type = {Applied Math.}, address = {Evanston, IL}, month = {June}, keywords = {}, } @preamble{ "\def\cprime{$'$} " } @article {Kirichenko97, AUTHOR = {Kirichenko, N. F.}, TITLE = {Analytical representation of perturbations of pseudo-inverse matrices}, JOURNAL = {Kibernet. Sistem. Anal.}, FJOURNAL = {Natsional\cprime naya Akademiya Nauk Ukrainy. Institut Kibernetiki im. V. M. Glushkova. Kibernetika i Sistemny\u\i\ Analiz}, YEAR = {1997}, NUMBER = {2}, PAGES = {98--107, 189}, MRCLASS = {15A09}, MRNUMBER = {98i:15009}, NOTE = {(English translation: Cybernet. Systems Anal. 33 (1997), no. 2, 230--238)}, } @article {Kirkland95, AUTHOR = {Kirkland, S. J.}, TITLE = {The group inverse associated with an irreducible periodic nonnegative matrix}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {16}, YEAR = {1995}, NUMBER = {4}, PAGES = {1127--1134}, MRCLASS = {15A09 (15A48 15A51)}, MRNUMBER = {96i:15005}, } @article {KirklandNeumann94, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {Convexity and concavity of the {P}erron root and vector of {L}eslie matrices with applications to a population model}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {15}, YEAR = {1994}, NUMBER = {4}, PAGES = {1092--1107}, MRCLASS = {92D25 (15A09 15A18)}, MRNUMBER = {95e:92015}, } @article {KirklandNeumann95, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {Group inverses of ${M}$-matrices associated with nonnegative matrices having few eigenvalues}, JOURNAL = LINAA1, VOLUME = {220}, YEAR = {1995}, PAGES = {181--213}, MRCLASS = {15A09 (15A18 15A48)}, MRNUMBER = {96c:15005}, } @article {KirklandNeumann98, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {The ${M}$-matrix group generalized inverse problem for weighted trees}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {19}, YEAR = {1998}, NUMBER = {1}, PAGES = {226--234 (electronic)}, MRCLASS = {05C50 (15A09 15A57)}, MRNUMBER = {99d:05062}, } @article {KirklandNeumann99, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {On group inverses of ${M}$-matrices with uniform diagonal entries}, JOURNAL = LINAA1, VOLUME = {296}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {153--170}, MRCLASS = {65Fxx (15A09)}, MRNUMBER = {1 713 277}, } @article {KirklandNeumann99a, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {Cutpoint decoupling and first passage times for random walks on graphs}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {20}, YEAR = {1999}, NUMBER = {4}, PAGES = {860--870 (electronic)}, MRCLASS = {60J10 (15A51 60G50)}, MRNUMBER = {2000f:60106}, } @article {KirklandNeumann00, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {Regular {M}arkov chains for which the transition matrix has large exponent}, JOURNAL = LINAA1, VOLUME = {316}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {45--65}, MRCLASS = {60J10}, MRNUMBER = {1 782 416}, } @article {KirklandNeumann00a, AUTHOR = {Kirkland, S. J. and Neumann, M.}, TITLE = {Extremal first passage times for trees}, JOURNAL = LINMA, VOLUME = {48}, YEAR = {2000}, PAGES = {21--33}, } @article {KirklandEtAl97, AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.}, TITLE = {Distances in weighted trees and group inverse of {L}aplacian matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {18}, YEAR = {1997}, NUMBER = {4}, PAGES = {827--841}, MRCLASS = {15A09 (05C50)}, MRNUMBER = {98h:15005}, } @article {KirklandEtAl98, AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.}, TITLE = {Bounds on the subdominant eigenvalue involving group inverses with applications to graphs}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {48(123)}, YEAR = {1998}, NUMBER = {1}, PAGES = {1--20}, MRCLASS = {15A18}, MRNUMBER = {99b:15010}, } @article {KirklandEtAl98a, AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.}, TITLE = {On a bound on algebraic connectivity: the case of equality}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {48(123)}, YEAR = {1998}, NUMBER = {1}, PAGES = {65--76}, MRCLASS = {15A45 (15A51 60J10)}, MRNUMBER = {99c:15034}, } @article {KirklandEtAl98b, AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.}, TITLE = {Applications of {P}az's inequality to perturbation bounds for {M}arkov chains}, JOURNAL = LINAA1, VOLUME = {268}, YEAR = {1998}, PAGES = {183--196}, MRCLASS = {15A51 (15A12 60J10)}, MRNUMBER = {99a:15007}, } @incollection {Kishi64, AUTHOR = {Kishi, F. H.}, TITLE = {On line computer control techniques and their application to re--entry aerospace vehicle control}, BOOKTITLE = {Advances in {C}ontrol {S}ystems {T}heory and {A}pplications (C. T. Leondes, Editor)}, PAGES = {245--257}, PUBLISHER = {Academic Press}, YEAR = {1964}, ADDRESS = {New York}, } @preamble{ "\def\cprime{$'$} " } @incollection {Kislovskaya87, AUTHOR = {Kislovskaya, N. M.}, TITLE = {A pseudo-inverse matrix and multiplicative groups of matrices}, BOOKTITLE = {Algorithmic and {N}umerical {P}roblems in {A}lgebra and {N}umber {T}heory ({R}ussian)}, PAGES = {40--52, 88}, PUBLISHER = {Akad. Nauk SSSR Dal\cprime nevostochn. Otdel.}, ADDRESS = {Vladivostok}, YEAR = {1987}, MRCLASS = {15A09 (20H20)}, MRNUMBER = {90m:15008}, } @article{Klee62, author = {Klee, V.}, year = {1962}, title = {Review of `Linearity of Best Approximations: A Characterization of Ellipsoids' ({Rudin} and {Smith})}, journal = {Math. Reviews}, volume = {23}, pages = {A2028}, KEYWORDS = {math, ginv, best approximation}, } @article{Klinger68, author = {Klinger, A.}, year = {1968}, title = {Approximate pseudoinverse solutions to ill--conditioned linear systems}, journal = {J. Optimization Th. Appl.}, volume = {2}, pages = {117--128}, } @TECHREPORT{KnyazevArgentati00, author = {Knyazev, A. V. and Argentati, M. E.}, title = {An Effective and Robust Algorithm for Finding Principal Angles Between Subspaces Using An {A}-Based Scalar Product}, institution = {Center for Computational Mathematics, University of Colorado at Denver}, year = {2000}, number = {163}, month = {August}, KEYWORDS = {geoa}, } @article {Koecher85, AUTHOR = {Koecher, M.}, TITLE = {The generalized inverse of integral matrices}, JOURNAL = LINAA1, VOLUME = {71}, YEAR = {1985}, PAGES = {187--198}, MRCLASS = {15A09 (15A36)}, MRNUMBER = {87b:15007}, } @article{Kogbetliantz55, author = {Kogbetliantz, E. G.}, year = {1955}, title = {Solution of Linear Systems by Diagonalization of Coefficients Matrix}, journal = {Quarterly of Applied Mathematics}, volume = {13}, pages = {123--132}, kwds = {nla, Kogbetliantz algorithm, svd}, } @article {Koliha74, AUTHOR = {Koliha, J. J.}, TITLE = {Pseudo-inverses of operators}, JOURNAL = BULAM1, VOLUME = {80}, YEAR = {1974}, PAGES = {325--328}, MRCLASS = {47A05}, MRNUMBER = {49 \#1153}, } @article {Koliha74a, AUTHOR = {Koliha, J. J.}, TITLE = {Power convergence and pseudoinverses of operators in {B}anach spaces}, JOURNAL = JMATA, VOLUME = {48}, YEAR = {1974}, PAGES = {446--469}, MRCLASS = {47A50}, MRNUMBER = {52 \#15055}, } @article {Koliha75, AUTHOR = {Koliha, J. J.}, TITLE = {The product of relatively regular operators}, JOURNAL = {Comment. Math. Univ. Carolinae}, VOLUME = {16}, YEAR = {1975}, NUMBER = {3}, PAGES = {531--539}, MRCLASS = {47A60}, MRNUMBER = {52 \#1373}, } @article {Koliha96, AUTHOR = {Koliha, J. J.}, TITLE = {A generalized {D}razin inverse}, JOURNAL = {Glasgow Math. J.}, VOLUME = {38}, YEAR = {1996}, NUMBER = {3}, PAGES = {367--381}, MRCLASS = {46H05 (15A09 16U60 34G10 47A05 47N20)}, MRNUMBER = {98b:46065}, } @article {Koliha99, AUTHOR = {Koliha, J. J.}, TITLE = {A simple proof of the product theorem for {E}{P} matrices}, JOURNAL = LINAA1, VOLUME = {294}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {213--215}, MRCLASS = {15A09 (15A27)}, MRNUMBER = {2000c:15003}, } @article {Koliha99a, AUTHOR = {Koliha, J. J.}, TITLE = {The {D}razin and {M}oore--{P}enrose inverse in ${C}\sp \ast$-algebras}, JOURNAL = {Math. Proc. R. Ir. Acad.}, VOLUME = {99A}, YEAR = {1999}, NUMBER = {1}, PAGES = {17--27}, MRCLASS = {}, MRNUMBER = {}, } @article {Koliha00, AUTHOR = {Koliha, J. J.}, TITLE = {Elements of ${C}\sp \ast$-algebras commuting with their {M}oore-{P}enrose inverse}, JOURNAL = {Studia Math.}, VOLUME = {139}, YEAR = {2000}, NUMBER = {1}, PAGES = {81--90}, MRCLASS = {46L05 (46H30 47A05)}, MRNUMBER = {2001b:46087}, } @article {Koliha01, AUTHOR = {Koliha, J. J.}, TITLE = {Continuity and differentiability of the {M}oore--{P}enrose inverse in ${C}\sp \ast$-algebras}, JOURNAL = {Math. Scand.}, VOLUME = {88}, YEAR = {2001}, NUMBER = {1}, PAGES = {154--160}, MRCLASS = {}, MRNUMBER = {}, } @article {Koliha01a, AUTHOR = {Koliha, J. J.}, TITLE = {Range projections of idempotents in ${C}\sp \ast$-algebras}, JOURNAL = {Demonstratio Math.}, VOLUME = {34}, YEAR = {2001}, NUMBER = {1}, PAGES = {91--103}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {simple proofs of results on Moore-Penrose inverse}, } @article {Koliha01b, AUTHOR = {Koliha, J. J.}, TITLE = {Block diagonalization}, JOURNAL = {Math. Bohem.}, VOLUME = {126}, YEAR = {2001}, NUMBER = {1}, PAGES = {237--246}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {new characterization of eigenprojection and Drazin inverse}, } @article {Koliha02, AUTHOR = {Koliha, J. J.}, TITLE = {Error bounds for a general perturbation of the {D}razin inverse}, JOURNAL = {Appl. Math. Comput.}, VOLUME = {126}, YEAR = {2002}, NUMBER = {2-3}, PAGES = {61--65}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {new characterization of eigenprojection and Drazin inverse}, } @article {KolihaRakocevic98, AUTHOR = {Koliha, J. J. and Rako{\v{c}}evi{\'c}, V.}, TITLE = {Continuity of the {D}razin inverse. {I}{I}}, JOURNAL = {Studia Math.}, VOLUME = {131}, YEAR = {1998}, NUMBER = {2}, PAGES = {167--177}, MRCLASS = {47A05 (46H05 47A53)}, MRNUMBER = {2000b:47004}, } @article {KolihaStraskraba99, AUTHOR = {Koliha, J. J. and Stra{\v{s}}kraba, I.}, TITLE = {Power bounded and exponentially bounded matrices}, JOURNAL = {Appl. Math.}, FJOURNAL = {Applications of Mathematics}, VOLUME = {44}, YEAR = {1999}, NUMBER = {4}, PAGES = {289--308}, MRCLASS = {34D05 (15A09 34E15 39A11)}, MRNUMBER = {2000h:34081}, } @article {KolihaTran99, AUTHOR = {Koliha, J. J. and Tran, T. D.}, TITLE = {Semistable operators and singularly perturbed differential equations}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {231}, YEAR = {1999}, NUMBER = {2}, PAGES = {446--458}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Drazin inverse of operators}, } @article {Koranyi00, AUTHOR = {Kor{\'a}nyi, A.}, TITLE = {Around the finite--dimensional spectral theorem}, JOURNAL = AMEMM, VOLUME = {108}, YEAR = {2001}, PAGES = {120--125}, } @book {KorganoffPavel-Parvu67, AUTHOR = {Korganoff, A. and Pavel-Parvu, M.}, TITLE = {M\'ethodes de calcul num\'erique. {T}ome {I}{I}: \'{E}l\'ements de th\'eorie des matrices carr\'ees et rectangles en analyse num\'erique}, PUBLISHER = {Dunod}, ADDRESS = {Paris}, YEAR = {1967}, PAGES = {xx+441}, MRCLASS = {65.35}, MRNUMBER = {34 \#7000}, } @incollection {Korsukov76, AUTHOR = {Korsukov, V. M.}, TITLE = {An application of iteration methods to the computation of semi-inverses of matrices}, BOOKTITLE = {Optimization {M}ethods and {O}perations {R}esearch, {A}pplied {M}athematics ({R}ussian)}, PAGES = {171--173, 191}, PUBLISHER = {Akad. Nauk SSSR Sibirsk. Otdel. Sibirsk. \`Energet. Inst., Irkutsk}, YEAR = {1976}, MRCLASS = {65K05}, MRNUMBER = {58 \#3442}, } @incollection {Korsukov82, AUTHOR = {Korsukov, V. M.}, TITLE = {Some properties of generalized inverse matrices}, BOOKTITLE = {Degenerate {S}ystems of {O}rdinary {D}ifferential {E}quations}, PAGES = {19--37}, PUBLISHER = {``Nauka'' Sibirsk. Otdel.}, ADDRESS = {Novosibirsk}, YEAR = {1982}, MRCLASS = {15A09}, MRNUMBER = {85f:15004}, } @article {KoshyTewarson85, AUTHOR = {Koshy, M. and Tewarson, R. P.}, TITLE = {On the use of restricted pseudo-inverses for the unified derivation of quasi-{N}ewton updates}, JOURNAL = {IMA J. Numer. Anal.}, VOLUME = {5}, YEAR = {1985}, NUMBER = {2}, PAGES = {141--151}, MRCLASS = {65H10 (65J10)}, MRNUMBER = {86g:65104}, } @incollection {KostinEtAl95, AUTHOR = {Kostin, V. I. and Khajdukov, V. G. and Tcheverda, V. A.}, TITLE = {On $r$-solutions of nonlinear equations}, BOOKTITLE = {Advanced {M}athematics: {C}omputations and {A}pplications (Novosibirsk, 1995)}, PAGES = {286--291}, PUBLISHER = {NCC Publ., Novosibirsk}, YEAR = {1995}, MRCLASS = {65J15}, MRNUMBER = {1 701 443}, } @article {KostinEtAl97, AUTHOR = {Kostin, V. I. and Khajdukov, V. G. and Tcheverda, V. A.}, TITLE = {$r$-solutions of equations of the first kind with a compact operator in {H}ilbert spaces: existence and stability}, JOURNAL = {Dokl. Akad. Nauk}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Doklady Akademii Nauk}, VOLUME = {355}, YEAR = {1997}, NUMBER = {3}, PAGES = {308--312}, MRCLASS = {47A50 (65J10 65J20)}, MRNUMBER = {98j:47021}, } @article {KourouklisPaige81, AUTHOR = {Kourouklis, S. and Paige, C. C.}, TITLE = {A constrained least squares approach to the general {G}auss-{M}arkov linear model}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {76}, YEAR = {1981}, NUMBER = {375}, PAGES = {620--625}, MRCLASS = {62J05}, MRNUMBER = {82m:62147}, KEYWORDS = {General Gauss-Markov linear model, constrained least-squares, numerical stability}, } @article {Krafft98, AUTHOR = {Krafft, O.}, TITLE = {An arithmetic-harmonic-mean inequality for nonnegative definite matrices}, JOURNAL = LINAA1, VOLUME = {268}, YEAR = {1998}, PAGES = {243--246}, MRCLASS = {15A45 (15A09 15A48)}, MRNUMBER = {98m:15034}, } @incollection {Krajewski84, AUTHOR = {Krajewski, W.}, TITLE = {Aggregation of models with restricted domains: an application of the pseudo-inverses}, BOOKTITLE = {Large {S}cale {S}ystems: {T}heory and {A}pplications 1983 ({W}arsaw, 1983)}, PAGES = {201--205}, PUBLISHER = {IFAC}, ADDRESS = {Laxenburg}, YEAR = {1984}, MRCLASS = {90A15 (90A16)}, MRNUMBER = {88m:90035}, } @article {KreijgerNeudecker77, AUTHOR = {Kreijger, R. G. and Neudecker, H.}, TITLE = {Exact linear restrictions on parameters in the general linear model with a singular covariance matrix}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {72}, YEAR = {1977}, NUMBER = {358}, PAGES = {430--432}, MRCLASS = {62J05}, MRNUMBER = {56 \#7029}, } @article {Krein47, AUTHOR = {Kre{\u\i}n, M. G.}, TITLE = {The theory of self-adjoint extensions of semi-bounded {H}ermitian transformations and its applications. {I}}, JOURNAL = {Rec. Math. [Mat. Sbornik] N.S.}, VOLUME = {20(62)}, YEAR = {1947}, PAGES = {431--495}, MRCLASS = {46.3X}, MRNUMBER = {9,515c}, } @article {Krein47a, AUTHOR = {Kre{\u\i}n, M. G.}, TITLE = {The theory of self-adjoint extensions of semi-bounded {H}ermitian transformations and its applications. {I}{I}}, JOURNAL = {Mat. Sbornik N.S.}, VOLUME = {21(63)}, YEAR = {1947}, PAGES = {365--404}, MRCLASS = {46.3X}, MRNUMBER = {9,515d}, } @article {Kress83, AUTHOR = {Kress, R.}, TITLE = {On the {F}redholm alternative}, JOURNAL = {Integral Equations Operator Theory}, VOLUME = {6}, YEAR = {1983}, NUMBER = {3}, PAGES = {453--457}, MRCLASS = {47B05}, MRNUMBER = {84f:47021}, } @article {Krishnamurthy83, AUTHOR = {Krishnamurthy, E. V.}, TITLE = {Fast parallel exact computation of the {M}oore-{P}enrose inverse and rank of a matrix}, JOURNAL = {Elektron. Informationsverarb. Kybernet.}, FJOURNAL = {Elektronische Informationsverarbeitung und Kybernetik}, VOLUME = {19}, YEAR = {1983}, NUMBER = {1-2}, PAGES = {95--98}, MRCLASS = {65F20 (65W05)}, MRNUMBER = {85h:65085}, } @incollection {Kruskal61, AUTHOR = {Kruskal, W.}, TITLE = {The coordinate-free approach to {G}auss-{M}arkov estimation, and its application to missing and extra observations}, BOOKTITLE = {Proc. 4th {B}erkeley {S}ympos. {M}ath. {S}tatist. and {P}rob., {V}ol. {I}}, PAGES = {435--451}, PUBLISHER = {Univ. California Press}, ADDRESS = {Berkeley, Calif.}, YEAR = {1961}, MRCLASS = {62.20 (62.55)}, MRNUMBER = {25 \#678}, } @article {Kruskal68, AUTHOR = {Kruskal, W.}, TITLE = {When are {G}auss-{M}arkov and least squares estimators identical? {A} coordinate-free approach}, JOURNAL = {Ann. Math. Statist}, VOLUME = {39}, YEAR = {1968}, PAGES = {70--75}, MRCLASS = {62.20}, MRNUMBER = {36 \#6047}, NOTE = {(see \cite{Haberman75})}, } @article {Kruskal75, AUTHOR = {Kruskal, W.}, TITLE = {The geometry of generalized inverses}, JOURNAL = {J. Roy. Statist. Soc. Ser. B}, VOLUME = {37}, YEAR = {1975}, PAGES = {272--283}, MRCLASS = {15A09}, MRNUMBER = {52 \#427}, NOTE = {(correction in \textit{J. Roy. Statist. Soc. Ser. B}\textbf{48}(1986), 258)}, } @article {Kuang82, AUTHOR = {Kuang, Jiao Xun}, TITLE = {The representation and approximation of {D}razin inverses of linear operators}, JOURNAL = {Numer. Math. J. Chinese Univ.}, FJOURNAL = {Numerical Mathematics. A Journal of Chinese Universities. Gaodeng Xuexiao Jisuan Shuxue Xuebao}, VOLUME = {4}, YEAR = {1982}, NUMBER = {2}, PAGES = {97--106}, MRCLASS = {47A05 (15A09)}, MRNUMBER = {84b:47001}, KEYWORDS = {Hilbert, Drazin, Newton method}, } @article {Kuang93, AUTHOR = {Kuang, Jiao Xun}, TITLE = {Approximate methods for generalized inverses of operators in {B}anach spaces}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications}, VOLUME = {11}, YEAR = {1993}, NUMBER = {4}, PAGES = {323--328}, MRCLASS = {47A05 (15A09 47A50 65J20)}, MRNUMBER = {94m:47005}, KEYWORDS = {Banach, Moore-Penrose, iterative method}, } @article {Kublanovskaya66, AUTHOR = {Kublanovskaya, V. N.}, TITLE = {On the calculation of generalized inverses and projections ({R}ussian)}, JOURNAL = {Z. Vycisl. Mat. i Mat. Fiz.}, VOLUME = {6}, YEAR = {1966}, PAGES = {326--332}, } @proceedings{Kuhn70, editor = {Kuhn, H. W.}, year = {1970}, title = {Proceedings {P}rinceton {S}ympos. {M}ath. {P}rog.}, publisher = {Princeton Univ. Press}, address = {Princeton, NJ}, } @article {KulkarniSivakumar95, AUTHOR = {Kulkarni, S. H. and Sivakumar, K. C.}, TITLE = {Applications of generalized inverses to interval linear programs in {H}ilbert spaces}, JOURNAL = {Numer. Funct. Anal. Optim.}, VOLUME = {16}, YEAR = {1995}, NUMBER = {7-8}, PAGES = {965--973}, MRCLASS = {90C08 (90C48)}, MRNUMBER = {96k:90038}, } @article {KulkarniSivakumar96, AUTHOR = {Kulkarni, S. H. and Sivakumar, K. C.}, TITLE = {Explicit solutions of a special class of linear programming problems in {B}anach spaces}, JOURNAL = {Acta Sci. Math. (Szeged)}, VOLUME = {62}, YEAR = {1996}, NUMBER = {3-4}, PAGES = {457--465}, MRCLASS = {90C48 (90C08)}, MRNUMBER = {98b:90170}, } @article {KunkelMehrmann96, AUTHOR = {Kunkel, P. and Mehrmann, V.}, TITLE = {Generalized inverses of differential-algebraic operators}, JOURNAL = SIAJM1, VOLUME = {17}, YEAR = {1996}, NUMBER = {2}, PAGES = {426--442}, MRCLASS = {34A09 (47E05)}, MRNUMBER = {97a:34006}, KEYWORDS = {diff, lindif, appdif}, } @article {Kuo77, AUTHOR = {Kuo, I Wen}, TITLE = {The {M}oore-{P}enrose inverses of singular ${M}$-matrices}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {17}, YEAR = {1977}, NUMBER = {1}, PAGES = {1--14}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {57 \#12548}, } @ARTICLE{KuoMazda67, author = {Kuo, M. C. Y. and Mazda, L. F.}, title = {Mimimum energy problems in {H}ilbert function space}, journal = {J. Franklin Inst.}, year = {1967}, volume = {283}, pages = {38--54}, } @ARTICLE{Kurepa68, author = {Kurepa, S.}, title = {Generalized inverse of an operator with a closed range}, journal = {Glasnik Mat.}, year = {1968}, volume = {3}, number = {23}, pages = {207--214}, } @BOOK{Kutzler00, author = {Kutzler, B. and Kokol-Voljc, V.}, title = {Introduction to {D}erive 5}, publisher = {Texas Instruments}, year = {2000}, address = {Dallas, TX 75265}, url = {http://education.ti.com/product/pdf/gb/derive5bk.pdf}, } @article {LaBuddeVerma69, AUTHOR = {LaBudde, C. D. and Verma, G. R.}, TITLE = {On the computation of a generalized inverse of a matrix}, JOURNAL = {Quart. Appl. Math.}, VOLUME = {27}, YEAR = {1969}, PAGES = {391--395}, MRCLASS = {65.35}, MRNUMBER = {40 \#6755}, } @article {Lamond87, AUTHOR = {Lamond, B. F.}, TITLE = {An efficient factorization for the group inverse}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, VOLUME = {8}, YEAR = {1987}, NUMBER = {4}, PAGES = {797--808}, MRCLASS = {65F05 (65F20)}, MRNUMBER = {89b:65071}, } @article {Lamond89, AUTHOR = {Lamond, B. F.}, TITLE = {A generalized inverse method for asymptotic linear programming}, JOURNAL = {Math. Programming}, VOLUME = {43}, YEAR = {1989}, NUMBER = {1 (Ser. A)}, PAGES = {71--86}, MRCLASS = {90C05 (65F05 65K05)}, MRNUMBER = {90d:90046}, } @article {LamondPuterman89, AUTHOR = {Lamond, B. F. and Puterman, M. L.}, TITLE = {Generalized inverses in discrete time {M}arkov decision processes}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {10}, YEAR = {1989}, NUMBER = {1}, PAGES = {118--134}, MRCLASS = {90C40 (15A09)}, MRNUMBER = {90c:90233}, } @ARTICLE{Lancaster70, author = {Lancaster, P.}, title = {Explicit solutions of linear matrix equations}, journal = SIAMR, year = {1970}, volume = {12}, pages = {544--566}, } @article{Lancaster77, author = {Lancaster, P.}, year = {1977}, title = {A Fundamental Theorem on Lambda-Matrices with Applications---{I}\@. Ordinary Differential Equations with Constant Coefficients}, journal = LINAA1, volume = {18}, pages = {189--211}, kwds = {la, lambda matrix, ode}, } @article{Lancaster77a, author = {Lancaster, P.}, year = {1977}, title = {A Fundamental Theorem on Lambda-Matrices with Applications---{II}\@. Difference Equations with Constant Coefficients}, journal = LINAA1, volume = {18}, pages = {213--222}, kwds = {la, lambda matrix, difference equation}, } @article{LancasterRokne77, author = {Lancaster, P. and Rokne, J. G.}, year = {1977}, title = {Solutions of Nonlinear Operator Equations}, journal = {SIAM Journal on Mathematical Analysis}, volume = {8}, pages = {448--457}, kwds = {nlop, matrix polynomial}, } @BOOK{LancasterTismenetsky85, author = {Lancaster, P. and Tismenetsky, M.}, title = {The {T}heory of {M}atrices ({S}econd {E}dition)}, publisher = {Academic Press}, year = {1985}, address = {San Diego}, ISBN = {0-12-435560-9}, } @ARTICLE{Lanczos58, author = {Lanczos, C.}, title = {Linear systems in self--adjoint form}, journal = AMEMM, year = {1958}, volume = {65}, pages = {665--679}, } @BOOK{Lanczos61, author = {Lanczos, C.}, title = {Linear {D}ifferential {O}perators}, publisher = {D. Van Nostrand, Co.}, year = {1961}, address = {Princeton}, } @ARTICLE{Landesman67, author = {Landesman, E. M.}, title = {Hilbert--space methods in elliptic partial differential equations}, journal = PACJM, year = {1967}, volume = {21}, pages = {113--131}, } @article {LangEtAl98, AUTHOR = {Lang, P. M. and Brenchley, J. M. and Nieves, R. G. and Kalivas, J. H.}, TITLE = {Cyclic subspace regression}, JOURNAL = {J. Multivariate Anal.}, VOLUME = {65}, YEAR = {1998}, NUMBER = {1}, PAGES = {58--70}, MRCLASS = {62H25 (62H05)}, MRNUMBER = {2000d:62096}, } @ARTICLE{Langenhop67, author = {Langenhop, C. E.}, title = {On generalized inverses of matrices}, journal = SIAJA, year = {1967}, volume = {15}, pages = {1239--1246}, } @article{Langenhop71, author = {Langenhop, C. E.}, year = {1971}, title = {The {L}aurent Expansion for a Nearly Singular Matrix}, journal = LINAA1, volume = {4}, pages = {329--340}, kwds = {la, Laurent Expansion, geig}, } @article{Langenhop73, author = {Langenhop, C. E.}, year = {1973}, title = {On the Invertibiliby of a Nearly Singular Matrix}, journal = LINAA1, volume = {7}, pages = {361--365}, kwds = {la}, } @article {Lardy75, AUTHOR = {Lardy, L. J.}, TITLE = {A series representation for the generalized inverse of a closed linear operator}, JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)}, VOLUME = {58}, YEAR = {1975}, NUMBER = {2}, PAGES = {152--157}, MRCLASS = {47A50 (65J05)}, MRNUMBER = {57 \#13540}, } @article {Lardy77, AUTHOR = {Lardy, L. J.}, TITLE = {Some iterative methods for linear operator equations with applications to generalized inverses}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {32}, YEAR = {1977}, NUMBER = {3}, PAGES = {610--618}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {56 \#7175}, } @article {Larimore90, AUTHOR = {Larimore, W. E.}, TITLE = {Order-recursive factorization of the pseudoinverse of a covariance matrix}, JOURNAL = {IEEE Trans. Automat. Control}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control}, VOLUME = {35}, YEAR = {1990}, NUMBER = {12}, PAGES = {1299--1303}, ISSN = {0018-9286}, CODEN = {IETAA9}, MRCLASS = {93B17 (65F10 93B40)}, MRNUMBER = {91k:93026}, } @article {LaskyRavani00, AUTHOR = {Lasky, Ty A. and Ravani, B.}, TITLE = {Sensor-based path planning and motion control for a robotic system for roadway crack sealing}, JOURNAL = {IEEE Transactions on Control Systems Technology}, VOLUME = {8}, YEAR = {2000}, PAGES = {609--622}, } @article {LatawiecEtAl00, AUTHOR = {Latawiec, K. J. and Ba{\'n}ka, S. and Tokarzewski, J.}, TITLE = {Control Zeros and Nonminimum Phase LTI Mimo Systems}, JOURNAL = {Annual Reviews in Control}, VOLUME = {24}, YEAR = {2000}, NUMBER = {1}, PAGES = {105--112}, } @book {Laurent72, AUTHOR = {Laurent, P. {-J.}}, TITLE = {Approximation et {O}ptimisation. {C}ollection {E}nseignement des {S}ciences, No. 13}, PUBLISHER = {Hermann}, ADDRESS = {Paris}, YEAR = {1972}, PAGES = {xiii+531}, MRCLASS = {41-01}, MRNUMBER = {57 \#6947}, } @incollection {Laurent86, AUTHOR = {Laurent, P. {-J.}}, TITLE = {Quadratic convex analysis and splines}, BOOKTITLE = {Methods of {F}unctional {A}nalysis in {A}pproximation {T}heory (Bombay, 1985)}, PAGES = {17--43}, PUBLISHER = {Birkh\"auser}, ADDRESS = {Basel}, YEAR = {1986}, MRCLASS = {41A15 (41A65 49A50 49A55 90C25)}, MRNUMBER = {89f:41015}, } @article {LaursenMbekhta93, AUTHOR = {Laursen, K. B. and Mbekhta, M.}, TITLE = {Closed range multipliers and generalized inverses}, JOURNAL = {Studia Math.}, VOLUME = {107}, YEAR = {1993}, NUMBER = {2}, PAGES = {127--135}, MRCLASS = {47B48 (46H05 46L05 47A05)}, MRNUMBER = {94i:47052}, } @article {Lavoie80, AUTHOR = {Lavoie, J. {-L}.}, TITLE = {A determinantal inequality involving the {M}oore-{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {31}, YEAR = {1980}, PAGES = {77--80}, MRCLASS = {15A09 (15A45)}, MRNUMBER = {81g:15001}, } @book {LawsonHanson74, AUTHOR = {Lawson, C. L. and Hanson, R. J.}, TITLE = {Solving {L}east {S}quares {P}roblems}, PUBLISHER = {Prentice-Hall Inc.}, ADDRESS = {Englewood Cliffs, N.J.}, YEAR = {1974}, PAGES = {xii+340}, MRCLASS = {65F20}, MRNUMBER = {51 \#2270}, NOTE = {(reprinted, \textit{Classics in Applied Mathematics}, 15. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995. xii+337 pp)}, } @ARTICLE{Leach61, author = {Leach, E. B.}, title = {A note on inverse function theorems}, journal = PROAM, year = {1961}, volume = {12}, pages = {694--697}, keywords = {}, } @article {Leach63, AUTHOR = {Leach, E. B.}, TITLE = {On a related function theorem}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {14}, YEAR = {1963}, PAGES = {687--689}, MRCLASS = {46.45 (26.55)}, MRNUMBER = {27 \#4053}, } @article {Leamer81, AUTHOR = {Leamer, E. E.}, TITLE = {Coordinate--free ridge regression bounds}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {76}, YEAR = {1981}, NUMBER = {376}, PAGES = {842--849}, MRCLASS = {}, MRNUMBER = {}, } @article {Leamer87, AUTHOR = {Leamer, E. E.}, TITLE = {Errors in variables in linear systems}, JOURNAL = {Econometrica}, VOLUME = {55}, YEAR = {1987}, NUMBER = {4}, PAGES = {893--909}, MRCLASS = {62J05 (62P20)}, MRNUMBER = {88g:62139}, } @article {LendarisEtAl99, AUTHOR = {Lendaris, G. G. and Mathia, K. and Saeks, R.}, TITLE = {Linear {H}opfield networks and constrained optimization}, JOURNAL = {IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics }, VOLUME = {29}, YEAR = {1999}, PAGES = {114--118}, } @article {LengZhang99, AUTHOR = {Leng, G. {-S}. and Zhang, Y.}, TITLE = {Vertex Angles for Simplices}, JOURNAL = {Applied Mathematics Letters}, VOLUME = {12}, YEAR = {1999}, PAGES = {1--5}, } @PHDTHESIS{Lent71, author = {Lent, A. H.}, title = {Wiener--{H}opf {O}perators and {F}actorizations}, school = {Northwestern Univertsity}, year = {1971}, type = {Doctoral dissertation in Applied Mathematics}, address = {Evanston, IL}, month = {June}, } @preamble{ "\def\cprime{$'$} " } @article {Leonov85, AUTHOR = {Leonov, A. S.}, TITLE = {Approximate calculation of a pseudo-inverse matrix by means of the generalized residual principle}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {25}, YEAR = {1985}, NUMBER = {6}, PAGES = {933--935, 959}, MRCLASS = {65F20}, MRNUMBER = {86h:65055}, } @article {Leonov85a, AUTHOR = {Leonov, A. S.}, TITLE = {The method of a minimal pseudoinverse matrix for solving ill-posed problems of linear algebra}, JOURNAL = {Dokl. Akad. Nauk SSSR}, VOLUME = {285}, YEAR = {1985}, NUMBER = {1}, PAGES = {36--40}, ISSN = {0002-3264}, MRCLASS = {65F30 (15A06)}, NOTE = {(English translation: Soviet Math. Dokl. \textbf{32}(1985), no. 3, 628--632)}, MRNUMBER = {87b:65051}, } @preamble{ "\def\cprime{$'$} " } @article {Leonov87, AUTHOR = {Leonov, A. S.}, TITLE = {The method of a minimal pseudoinverse matrix}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {27}, YEAR = {1987}, NUMBER = {8}, PAGES = {1123--1138, 1276}, ISSN = {0044-4669}, MRCLASS = {65F20}, MRNUMBER = {89g:65048}, } @article {Leonov91, AUTHOR = {Leonov, A. S.}, TITLE = {On the theory of the method of the minimal pseudo-inverse matrix}, JOURNAL = {Dokl. Akad. Nauk SSSR}, FJOURNAL = {Doklady Akademii Nauk SSSR}, VOLUME = {314}, YEAR = {1990}, NUMBER = {1}, PAGES = {89--93}, MRCLASS = {65F20 (15A09)}, MRNUMBER = {92d:65067}, } @preamble{ "\def\cprime{$'$} " } @article {Leonov91a, AUTHOR = {Leonov, A. S.}, TITLE = {The minimal pseudo-inverse matrix method: theory and numerical realization}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {31}, YEAR = {1991}, NUMBER = {10}, PAGES = {1427--1443}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {92m:15004}, } @article {Leonov91b, AUTHOR = {Leonov, A. S.}, TITLE = {On the accuracy of the minimal pseudo-inverse matrix method}, JOURNAL = {Mat. Zametki}, FJOURNAL = {Akademiya Nauk SSSR. Matematicheskie Zametki}, VOLUME = {49}, YEAR = {1991}, NUMBER = {4}, PAGES = {81--87, 158}, MRCLASS = {65F20}, MRNUMBER = {92g:65046}, } @incollection {Leonov92, AUTHOR = {Leonov, A. S.}, TITLE = {The method of minimal pseudoinversed matrix. {B}asic statements}, BOOKTITLE = {Ill-{P}osed {P}roblems in {N}atural {S}ciences ({M}oscow, 1991)}, PAGES = {57--62}, PUBLISHER = {VSP}, ADDRESS = {Utrecht}, YEAR = {1992}, MRCLASS = {65F20 (65F30)}, MRNUMBER = {94h:65041}, } @TECHREPORT{LeringeWedin70, author = {Leringe, {\"O}. and Wedin, P.-{\AA}.}, title = {A comparison between different methods to compute a vector $\x$ which minimizes $\|{A}\x-\vect{b}\|_2$ when ${G}\x=\vect{h}$}, institution = {Lund University}, year = {1970}, type = {Department of Computer Science}, address = {Lund, Sweden}, month = {March}, keywords = {}, } @article {Lesnjak00, AUTHOR = {Le{\v{s}}njak, G.}, TITLE = {Semigroups of {E}{P} linear transformations}, JOURNAL = LINAA1, VOLUME = {304}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {109--118}, MRCLASS = {47A05 (15A09 47D03)}, MRNUMBER = {2001b:47003}, } @article {LevinBen-Israel01, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {Directional {N}ewton Methods in $n$ Variables}, JOURNAL = {Mathematics of Computations}, VOLUME = {}, YEAR = {2001}, NUMBER = {}, PAGES = {}, MRCLASS = {}, MRNUMBER = {}, URL = {http://rutcor.rutgers.edu/~bisrael/NEWTON-DIR.ps}, } @article {LevinBen-Israel01a, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {A {N}ewton Method for Systems of $m$ Equations in $n$ Variables}, JOURNAL = {Nonlinear Analysis}, VOLUME = {47}, YEAR = {2001}, NUMBER = {}, PAGES = {1961--1971}, MRCLASS = {}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/26.ps}, } @inproceedings {LevinBen-Israel01b, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {Directional {H}alley and Quasi-{H}alley Methods in $n$ Variables}, BOOKTITLE = {Inherently {P}arallel {A}lgorithms in {F}easibility and {O}ptimization and their {A}pplications}, EDITOR = {Butnariu, D. and Censor, Y. and Reich, S.}, PAGES = {}, PUBLISHER = {Elsevier Science}, ADDRESS = {Amsterdam}, YEAR = {2001}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/28.ps}, } @article {LevinBen-Israel01c, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {The {N}ewton Bracketing Method for Convex Minimization}, JOURNAL = {Computational Optimization and Applications}, VOLUME = {21}, YEAR = {2002}, NUMBER = {}, PAGES = {213--229}, MRCLASS = {}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/33.ps}, } @TECHREPORT{LevinBen-Israel02, author = {Levin, Y. and Ben-Israel, A.}, title = {Inverse-free Methods for Systems of Nonlinear Equations}, institution = {Rutgers University}, year = {2000}, type = {RUTCOR--Rutgers Ctr. Oper. Res.}, number = {58-2000}, address = {Piscataway, NJ}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/58.ps}, } @article {LevinEtAl01, AUTHOR = {Levin, Y. and Nediak, M. and Ben-Israel, A.}, TITLE = {A Direct Approach to Calculus of Variations via {N}ewton-{R}aphson Method}, JOURNAL = {Comput. \& Appl. Math.}, VOLUME = {139}, YEAR = {2001}, NUMBER = {}, PAGES = {197--213}, MRCLASS = {}, MRNUMBER = {}, } @article {LevineHartwig80, AUTHOR = {Levine, J. and Hartwig, R. E.}, TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {I}}, JOURNAL = {Cryptologia}, VOLUME = {4}, YEAR = {1980}, NUMBER = {2}, PAGES = {71--85}, MRCLASS = {94B99}, MRNUMBER = {81d:94028}, } @article {LevineHartwig80a, AUTHOR = {Levine, J. and Hartwig, R. E.}, TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {I}{I}}, JOURNAL = {Cryptologia}, VOLUME = {4}, YEAR = {1980}, NUMBER = {3}, PAGES = {150--168}, MRCLASS = {94B99}, MRNUMBER = {81j:94030}, } @article {Levy98, AUTHOR = {Levy, B. C.}, TITLE = {A note on the hyperbolic singular value decomposition}, JOURNAL = LINAA1, VOLUME = {277}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {135--142}, MRCLASS = {15A18}, MRNUMBER = {99b:15011}, } @article {Lewis95, AUTHOR = {Lewis, A. S.}, TITLE = {The convex analysis of unitarily invariant matrix functions}, JOURNAL = {J. Convex Anal.}, VOLUME = {2}, YEAR = {1995}, NUMBER = {1-2}, PAGES = {173--183}, MRCLASS = {49J52 (15A60 49N15 90C25)}, MRNUMBER = {96m:49033}, } @INPROCEEDINGS{LewisEtAl68, author = {Lewis, T. O. and Boullion, T. L. and Odell, P. L.}, crossref = {BoullionOdell68}, title = {A bibliography on generalized matrix inverses}, year = {1968}, pages = {283--315}, } @article {LewisNewman68, AUTHOR = {Lewis, T. O. and Newman, T. G.}, TITLE = {Pseudoinverses of positive semidefinite matrices}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {16}, YEAR = {1968}, PAGES = {701--703}, MRCLASS = {15.15}, MRNUMBER = {38 \#2147}, } @article {LewisOdell66, AUTHOR = {Lewis, T. O. and Odell, P. L.}, TITLE = {A generalization of the {G}auss-{M}arkov theorem}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {61}, YEAR = {1966}, PAGES = {1063--1066}, MRCLASS = {62.55}, MRNUMBER = {34 \#3720}, } @article {LiEtAl00, AUTHOR = {Li, Bin and Li, Yinghui and Ying, Xuegang}, TITLE = {Dynamic modeling and simulation of flexible cable with large sag}, JOURNAL = {Applied Mathematics and Mechanics (English Edition)}, VOLUME = {21}, YEAR = {2000}, PAGES = {707--714}, } @article {LiMathias00, AUTHOR = {Li, Chi-Kwong and Mathias, R.}, TITLE = {Extremal characterizations of the {S}chur complement and resulting inequalities}, JOURNAL = SIAMR, VOLUME = {42}, YEAR = {2000}, NUMBER = {2}, PAGES = {233--246 (electronic)}, MRCLASS = {15A42 (15A18 15A21 47A63)}, MRNUMBER = {1 778 353}, } @article {LiTsing88, AUTHOR = {Li, Chi-Kwong and Tsing, Nam-Kiu}, TITLE = {Some isometries of rectangular complex matrices}, JOURNAL = LINMA, VOLUME = {23}, YEAR = {1988}, NUMBER = {1}, PAGES = {47--53}, MRCLASS = {15A60}, MRNUMBER = {89g:15031}, } @article {Li93, AUTHOR = {Li, Ren Cang}, TITLE = {Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils}, JOURNAL = LINAA1, VOLUME = {182}, YEAR = {1993}, PAGES = {199--234}, MRCLASS = {15A60 (15A42 47A30 47A55 47A75)}, MRNUMBER = {94c:15040}, } @article {Li93a, AUTHOR = {Li, Ren-Cang}, TITLE = {A perturbation bound for the generalized polar decomposition}, JOURNAL = {BIT}, VOLUME = {33}, YEAR = {1993}, NUMBER = {2}, PAGES = {304--308}, MRCLASS = {15A23 (15A45)}, MRNUMBER = {96a:15011}, } @article {Li97, AUTHOR = {Li, Ren-Cang}, TITLE = {Relative perturbation theory. {I}{I}{I}. {M}ore bounds on eigenvalue variation}, JOURNAL = LINAA1, VOLUME = {266}, YEAR = {1997}, PAGES = {337--345}, MRCLASS = {15A18 (15A42 65F15)}, MRNUMBER = {99e:15013}, } @article {Li98, AUTHOR = {Li, Ren-Cang}, TITLE = {Relative perturbation theory. {I}. {E}igenvalue and singular value variations}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {19}, YEAR = {1998}, NUMBER = {4}, PAGES = {956--982 (electronic)}, MRCLASS = {15A18 (15A42 65F15 65F35)}, MRNUMBER = {99e:15012}, } @article {Li99, AUTHOR = {Li, Ren-Cang}, TITLE = {Relative perturbation theory. {I}{I}. {E}igenspace and singular subspace variations}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {20}, YEAR = {1999}, NUMBER = {2}, PAGES = {471--492 (electronic)}, MRCLASS = {65F15 (15A18 15A42 65F35)}, MRNUMBER = {99k:65034}, } @article {Li00, AUTHOR = {Li, Ren-Cang}, TITLE = {Relative perturbation theory. {I}{V}. $\sin 2\theta$ theorems}, JOURNAL = LINAA1, VOLUME = {311}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {45--60}, MRCLASS = {15A42 (15A18 47A55 65F15 65F35)}, MRNUMBER = {2001c:15025}, } @article {LiStewart00, AUTHOR = {Li, Ren-Cang and Stewart, G. W.}, TITLE = {A new relative perturbation theorem for singular subspaces}, JOURNAL = LINAA1, VOLUME = {313}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {41--51}, MRCLASS = {15A18 (15A42 65F15)}, MRNUMBER = {2001c:15013}, } @article {LiWei01, AUTHOR = {Li, Xiezhang and Wei, Yimin}, TITLE = {An improvement on the perturbation of the group inverse and oblique projection}, JOURNAL = LINAA1, VOLUME = {338}, YEAR = {2001}, PAGES = {53--66}, MRCLASS = {}, MRNUMBER = {}, } @article {LiangEtAl97, AUTHOR = {Liang, Ping and Chen, Su Huan and Huang, Cheng}, TITLE = {Moore--{P}enrose inverse method of topological variation of finite element systems}, JOURNAL = {Comput. \& Structures}, VOLUME = {62}, YEAR = {1997}, NUMBER = {2}, PAGES = {243--251}, MRCLASS = {73V05}, MRNUMBER = {97i:73098}, } @article {LiangYong92, AUTHOR = {Liang, Yi and Yong, Xue Rong}, TITLE = {Group inverses of block matrices}, JOURNAL = {J. Xinjiang Univ. Natur. Sci.}, FJOURNAL = {Xinjiang University. Journal. Natural Science Edition. Xinjiang Daxue Xuebao. Ziran Kexue Ban}, VOLUME = {9}, YEAR = {1992}, NUMBER = {4}, PAGES = {34--39}, MRCLASS = {15A09}, MRNUMBER = {94c:15002}, } @article {Liber54, AUTHOR = {Liber, A. E.}, TITLE = {On the theory of generalized groups}, JOURNAL = {Doklady Akad. Nauk SSSR (N.S.)}, VOLUME = {97}, YEAR = {1954}, PAGES = {25--28}, MRCLASS = {20.0X}, MRNUMBER = {16,9c}, KEYWORDS = {inverse semigroups}, } @article {Lika75, AUTHOR = {Lika, D. K.}, TITLE = {The application of generalized inverse operators in iteration processes}, JOURNAL = {Mat. Issled.}, VOLUME = {10}, YEAR = {1975}, NUMBER = {2(36)}, PAGES = {264--270, 289}, MRCLASS = {47H15 (65J05)}, MRNUMBER = {53 \#6379}, KEYWORDS = {Banach, Newton method}, } @article {LinLin90, AUTHOR = {Lin, Shwu-Yeng T. and Lin, You Feng}, TITLE = {The $n$-dimensional {P}ythagorean theorem}, JOURNAL = LINMA, VOLUME = {26}, YEAR = {1990}, NUMBER = {1-2}, PAGES = {9--13}, MRCLASS = {51M05}, MRNUMBER = {90k:51031}, NOTE = {(see \cite{Bhatia91})}, } @article {LinSanford, AUTHOR = {Lin, K. {-W.} and Sanford, A. R.}, TITLE = {Improving regional earthquake locations using a modified {G} matrix and fuzzy logic}, JOURNAL = {Bulletin of the Seismological Society of America}, VOLUME = {91}, YEAR = {2001}, NUMBER = {1-2}, PAGES = {82--93}, } @article {Liski96, AUTHOR = {Liski, E. P.}, TITLE = {On {L}{\"o}wner-ordering antitonicity of matrix inversion}, JOURNAL = {Acta Math. Appl. Sinica (English Ser.)}, FJOURNAL = {Acta Mathematicae Applicatae Sinica. English Series. Yingyong Shuxue Xuebao}, VOLUME = {12}, YEAR = {1996}, NUMBER = {4}, PAGES = {435--442}, MRCLASS = {15A09}, MRNUMBER = {98c:15015}, } @article {LiskiPuntanen89, AUTHOR = {Liski, E. P. and Puntanen, S.}, TITLE = {A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices}, JOURNAL = {Comm. Statist. Theory Methods}, VOLUME = {18}, YEAR = {1989}, NUMBER = {5}, PAGES = {1747--1751}, MRCLASS = {62H05 (15A09 62E10)}, MRNUMBER = {90k:62105}, } @article {LiskiWang94, AUTHOR = {Liski, E. P. and Wang, Song Gui}, TITLE = {Another look at the naive estimator in a regression model}, JOURNAL = {Metrika}, VOLUME = {41}, YEAR = {1994}, NUMBER = {1}, PAGES = {55--64}, MRCLASS = {62J05}, MRNUMBER = {95m:62140}, } @article {LiskiWang96, AUTHOR = {Liski, E. P. and Wang, Song Gui}, TITLE = {On the $\{2\}$-inverse and some ordering properties of nonnegative definite matrices}, JOURNAL = {Acta Math. Appl. Sinica (English Ser.)}, FJOURNAL = {Acta Mathematicae Applicatae Sinica. English Series. Yingyong Shuxue Xuebao}, VOLUME = {12}, YEAR = {1996}, NUMBER = {1}, PAGES = {22--27}, MRCLASS = {15A09}, MRNUMBER = {97d:15006}, } @article {Lister71, AUTHOR = {Lister, W. G.}, TITLE = {Ternary rings}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {154}, YEAR = {1971}, PAGES = {37--55}, MRCLASS = {16.96}, MRNUMBER = {42 \#7716}, } @article {LiuWang99, AUTHOR = {Liu, Jianzhou and Wang, Jian}, TITLE = {Some inequalities for {S}chur complements}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {293}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {233--241}, MRCLASS = {15A45 (15A57)}, MRNUMBER = {2000d:15016}, } @article {LiuLiu95, AUTHOR = {Liu, X. and Liu, D.}, TITLE = {Recursive computation of generalized inverses with application to optimal state estimation}, JOURNAL = {Control Theory Adv. Tech.}, FJOURNAL = {Control Theory and Advanced Technology}, VOLUME = {10}, YEAR = {1995}, PAGES = {1485--1497}, MRCLASS = {93E12 (93B40)}, MRNUMBER = {96i:93085}, } @ARTICLE{Locker67, author = {Locker, J.}, title = {An existence analysis for nonlinear equations in {H}ilbert space}, journal = TRAAM, year = {1967}, volume = {128}, pages = {403--413}, keywords = {}, } @ARTICLE{Locker70, author = {Locker, J.}, title = {An existence analysis for nonlinear boundary value problems}, journal = SIAJA, year = {1970}, volume = {19}, pages = {199--207}, } @ARTICLE{Lonseth54, author = {Lonseth, A. T.}, title = {Approximate solutions of {F}redholm--type integral equations}, journal = BULAM1, year = {1954}, volume = {60}, pages = {415--430}, } @article {LopezGuerra96, AUTHOR = {L{\'o}pez Estrada, Jes{\'u}s and Guerra Ones, Valia}, TITLE = {Numerical calculation of the pseudoinverse using {L}eonov's minimal method}, JOURNAL = {Investigaci\'on Oper.}, FJOURNAL = {Investigaci\'on Operacional. Revista}, VOLUME = {17}, YEAR = {1996}, NUMBER = {1-3}, PAGES = {139--147}, ISSN = {0257-4306}, MRCLASS = {65F20}, MRNUMBER = {99e:65068}, } @article {LopezGuerra00, AUTHOR = {L{\'o}pez Estrada, Jes{\'u}s and Guerra Ones, Valia}, TITLE = {Maximum Balance Criterion for Choosing the Parameter $\lambda$ in the Minimal Pseudoinverse Method}, JOURNAL = {Revista Investigaci{\'o}n Operacional}, VOLUME = {21}, YEAR = {2000}, PAGES = {}, MRCLASS = {}, NOTE = {}, } @article {LopezEtAl96, AUTHOR = {L{\'o}pez Estrada, Jes{\'u}s and Madrid de la Vega, Humberto and Guerra Ones, Valia}, TITLE = {Numerical calculation of the {M}oore-{P}enrose pseudoinverse of a matrix}, JOURNAL = {Investigaci\'on Oper.}, FJOURNAL = {Investigaci\'on Operacional. Revista}, VOLUME = {17}, YEAR = {1996}, NUMBER = {1-3}, PAGES = {117--132}, MRCLASS = {65F20}, MRNUMBER = {99e:65067}, } @article {Loud61, AUTHOR = {Loud, W. S.}, TITLE = {Some singular cases of the implicit function theorem}, JOURNAL = {Amer. Math. Monthly}, VOLUME = {68}, YEAR = {1961}, PAGES = {965--977}, MRCLASS = {26.55}, MRNUMBER = {34 \#7744}, } @ARTICLE{Loud66, author = {Loud, W. S.}, title = {Generalized inverses and generalized {G}reen's functions}, journal = SIAJA, year = {1966}, volume = {14}, pages = {342--369}, } @ARTICLE{Loud70, author = {Loud, W. S.}, title = {Some examples of generalized {G}reen's functions and generalized {G}reen's matrices}, journal = SIAMR, year = {1970}, volume = {12}, pages = {194--210}, } @article {Loud80, AUTHOR = {Loud, W. S.}, TITLE = {A bifurcation application of the generalized inverse of a linear differential operator}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {11}, YEAR = {1980}, NUMBER = {3}, PAGES = {545--558}, MRCLASS = {47A05 (34B15 34C25 47H15)}, MRNUMBER = {83b:47002}, } @article {Lovass-NagyEtAl77, AUTHOR = {Lovass--Nagy, V. and Miller, R. J. and Powers, D. L.}, TITLE = {On system realization by matrix generalized inverses}, JOURNAL = {Internat. J. Control}, VOLUME = {26}, YEAR = {1977}, NUMBER = {5}, PAGES = {745--751}, MRCLASS = {93B15}, MRNUMBER = {56 \#14890}, NOTE = {(see correction in \cite{EitelbergHanselmann78})}, } @article {Lovass-NagyPowers71, AUTHOR = {Lovass-Nagy, V. and Powers, D. L.}, TITLE = {On the commuting reciprocal inverse of some partitioned matrices}, JOURNAL = LINAA1, VOLUME = {4}, YEAR = {1971}, PAGES = {183--190}, MRCLASS = {15.15}, MRNUMBER = {44 \#1675}, } @article {Lovass-NagyPowers73, AUTHOR = {Lovass--Nagy, V. and Powers, D. L.}, TITLE = {A relation between the {M}oore-{P}enrose and commuting reciprocal inverses}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {24}, YEAR = {1973}, PAGES = {44--49}, MRCLASS = {15A09}, MRNUMBER = {47 \#6722}, } @article {Lovass-NagyPowers73a, AUTHOR = {Lovass--Nagy, V. and Powers, D. L.}, TITLE = {A note on the ``${Y}$-inverse'' of a matrix}, JOURNAL = {Internat. J. Control (1)}, VOLUME = {18}, YEAR = {1973}, PAGES = {1113--1115}, MRCLASS = {15A09 (93E10)}, MRNUMBER = {49 \#10713}, } @article {Lovass-NagyPowers74, AUTHOR = {Lovass--Nagy, V. and Powers, D. L.}, TITLE = {On a relation among generalized inverses, with application to the {M}oore-{P}enrose inverse of certain {T}oeplitz matrices}, JOURNAL = {Indust. Math.}, VOLUME = {24}, YEAR = {1974}, PAGES = {67--76}, MRCLASS = {15A09}, MRNUMBER = {52 \#5698}, } @article {Lovass-NagyPowers75, AUTHOR = {Lovass--Nagy, V. and Powers, D. L.}, TITLE = {Matrix generalized inverses in the handling of control problems containing input derivatives}, JOURNAL = {Internat. J. Systems Sci.}, VOLUME = {6}, YEAR = {1975}, PAGES = {693--696}, MRCLASS = {93C05}, MRNUMBER = {52 \#2668}, } @article {Lovass-NagyPowers75a, AUTHOR = {Lovass--Nagy, V. and Powers, D. L.}, TITLE = {On rectangular systems of differential equations and their application to circuit theory}, JOURNAL = {J. Franklin Inst.}, VOLUME = {299}, YEAR = {1975}, NUMBER = {6}, PAGES = {399--407}, MRCLASS = {34A30}, MRNUMBER = {51 \#8513}, } @article {Lowdin62, AUTHOR = {L{\"o}wdin, Per-Olov}, TITLE = {Studies in perturbation theory. {I}{V}. {S}olution of eigenvalue problem by projection operator formalism}, JOURNAL = {J. Mathematical Phys.}, VOLUME = {3}, YEAR = {1962}, PAGES = {969--982}, MRCLASS = {81.41}, MRNUMBER = {26 \#4714}, } @article {Lowerre74, AUTHOR = {Lowerre, J. M.}, TITLE = {Some relationships between ${\rm {B}{L}{U}{E}}$s, ${\rm {W}{I}{S}{E}}$s and ${\rm {S}{L}{S}{E}}$s}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {69}, YEAR = {1974}, PAGES = {223--225}, MRCLASS = {62J05}, MRNUMBER = {52 \#7031}, KEYWORDS = {Lin model, BLUE, Weighted LS, linear regression}, NOTE = {(see \cite{BaksalaryKala83a})}, } @article {Lowerre77, AUTHOR = {Lowerre, J. M.}, TITLE = {Some simplifying results on {B}{L}{U}{E}s}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {72}, YEAR = {1977}, NUMBER = {358}, PAGES = {433--437}, MRCLASS = {62F10 (62J05)}, MRNUMBER = {56 \#4025}, KEYWORDS = {Lin model, BLUE, estimation, linear regression}, } @article {Lowner34, AUTHOR = {L{\"o}wner, K.}, TITLE = {{\"U}ber monotone {M}atrixfunktionen}, JOURNAL = {Math. Z.}, VOLUME = {38}, YEAR = {1934}, PAGES = {177--216}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {Lowner ordering}, } @ARTICLE{LuSWangG93, AUTHOR = {Lu, Senquan and Wang, Guorong}, TITLE = {A parallel algorithm for computing the minimum $N$-norm $M$-least squares solution to an inconsistent system of linear equations (Chinese)}, JOURNAL = {J. Shanghai Teachers University}, FJOURNAL = {Journal of Shanghai Teachers University. Natural Sciences}, VOLUME = {22}, YEAR = {1993}, NUMBER = {2}, PAGES = {1--7}, MRCLASS = {65F05 (65Y05)}, MRNUMBER = {1 263 004} } @article {Lu87, AUTHOR = {Lu, Shi Jie}, TITLE = {The range and pseudo-inverse of a product}, JOURNAL = {Tohoku Math. J. (2)}, FJOURNAL = {The Tohoku Mathematical Journal. Second Series}, VOLUME = {39}, YEAR = {1987}, NUMBER = {1}, PAGES = {89--94}, MRCLASS = {47A05}, MRNUMBER = {87m:47005}, } @article {Lu88, AUTHOR = {Lu, Shi Jie}, TITLE = {An application of pseudo-inverses---the analytic characteristic of ${T}$-regular points for closed operators}, JOURNAL = {Tohoku Math. J. (2)}, FJOURNAL = {The Tohoku Mathematical Journal. Second Series}, VOLUME = {40}, YEAR = {1988}, NUMBER = {3}, PAGES = {331--341}, MRCLASS = {47A05 (47A10)}, MRNUMBER = {89g:47004}, } @article {Luecke79, AUTHOR = {Luecke, G. R.}, TITLE = {A numerical procedure for computing the {M}oore-{P}enrose inverse}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {32}, YEAR = {1979}, NUMBER = {2}, PAGES = {129--137}, MRCLASS = {65F20}, MRNUMBER = {80h:65024}, } @incollection {Lukacs89, AUTHOR = {Luk{\'a}cs, G.}, TITLE = {The generalized inverse matrix and the surface-surface intersection problem}, BOOKTITLE = {Theory and {P}ractice of {G}eometric {M}odeling ({B}laubeuren, 1988)}, PAGES = {167--185}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1989}, MRCLASS = {65D17 (53A05 65H99)}, MRNUMBER = {91f:65041}, } @article {LyashkoEtAl85, AUTHOR = {Lyashko, I. I. and Kudrinski{\u\i}, V. Yu. and Ostapchuk, V. S.}, TITLE = {A method for determining the generalized normal solution of a system of linear algebraic equations}, JOURNAL = {Dokl. Akad. Nauk Ukrain. SSR Ser. A}, FJOURNAL = {Akademiya Nauk Ukrainsko\u\i\ SSR. Doklady. Seriya A. Fiziko-Matematicheskie i Tekhnicheskie Nauki}, YEAR = {1985}, NUMBER = {7}, PAGES = {16--20}, MRCLASS = {65F05 (15A06)}, MRNUMBER = {87c:65033}, } @BOOK{MacDuffee56, author = {MacDuffee, C. C.}, title = {The {T}heory of {M}atrices}, publisher = {Chelsea}, year = {1956}, address = {New York}, keywords = {}, } @article {Machalova00, AUTHOR = {Machalov{\'a}, Jitka}, TITLE = {Chipman pseudoinverse of matrix, its computation and application in spline theory}, JOURNAL = {Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math.}, FJOURNAL = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica}, VOLUME = {39}, YEAR = {2000}, PAGES = {143--157}, MRCLASS = {65F20 (65D07)}, MRNUMBER = {1 826 358}, } @article {Maess79, AUTHOR = {Mae{\ss}, G.}, TITLE = {A projection method solving general linear algebraic equations}, JOURNAL = {Rostock. Math. Kolloq.}, VOLUME = {12}, YEAR = {1979}, PAGES = {77--85}, MRCLASS = {65F20}, KEYWORDS = {compit, lineq, proj, compar}, MRNUMBER = {80k:65040}, NOTE = {(extension of results of \cite{Tanabe71})}, } @inproceedings {Maess84, AUTHOR = {Mae{\ss}, G.}, TITLE = {Iterative solution of rectangular systems of linear algebraic equations}, BOOKTITLE = {Computational {M}athematics ({W}arsaw, 1980)}, PAGES = {527--533}, PUBLISHER = {PWN}, ADDRESS = {Warsaw}, YEAR = {1984}, MRCLASS = {65F10}, MRNUMBER = {86j:65041}, KEYWORDS = {compit, lineq}, } @article {MaessPeters78, AUTHOR = {Mae{\ss}, G. and Peters, W.}, TITLE = {L\"osung inkonsistenter linearer {G}leichungssysteme und {B}estimmung einer {P}seudoinversen f\"ur rechteckige {M}atrizen durch {S}paltenapproximation}, JOURNAL = ZANGM1, VOLUME = {58}, YEAR = {1978}, NUMBER = {4}, PAGES = {233--237}, MRCLASS = {65F20}, MRNUMBER = {58 \#24886}, KEYWORDS = {compit, proj, invMP, invo, sollsq}, } @book {MagnusNeudecker99, AUTHOR = {Magnus, J. R. and Neudecker, H.}, TITLE = {Matrix {D}ifferential {C}alculus with {A}pplications in {S}tatistics and {E}conometrics}, PUBLISHER = {John Wiley \& Sons Ltd.}, ADDRESS = {Chichester}, YEAR = {1999}, PAGES = {xviii+395}, ISBN = {0-471-98633-X}, MRCLASS = {15-01 (26-01 62-01)}, MRNUMBER = {2000d:15001}, NOTE = {(revised reprint of the 1988 original)}, } @article {Maher90, AUTHOR = {Maher, P. J.}, TITLE = {Some operator inequalities concerning generalized inverses}, JOURNAL = {Illinois J. Math.}, VOLUME = {34}, YEAR = {1990}, NUMBER = {3}, PAGES = {503--514}, MRCLASS = {47A30 (47A05 47B10)}, MRNUMBER = {91c:47011}, } @article {Maher92, AUTHOR = {Maher, P. J.}, TITLE = {Some norm inequalities concerning generalized inverses}, JOURNAL = LINAA1, VOLUME = {174}, YEAR = {1992}, PAGES = {99--110}, MRCLASS = {47A30 (15A09 47A05 47A62 47B10)}, MRNUMBER = {93d:47016}, } @article {Makelainen70, AUTHOR = {M{\"a}kel{\"a}inen, T.}, TITLE = {Projections and generalized inverses in the general linear model}, JOURNAL = {Soc. Sci. Fenn. Comment. Phys.-Math.}, VOLUME = {38}, YEAR = {1970}, PAGES = {13--25}, MRCLASS = {15.15}, MRNUMBER = {41 \#219}, } @article {Mangasarian68, AUTHOR = {Mangasarian, O. L.}, TITLE = {Characterizations of real matrices of monotone kind}, JOURNAL = {SIAM Rev.}, VOLUME = {10}, YEAR = {1968}, PAGES = {439--441}, MRCLASS = {15.60}, MRNUMBER = {38 \#5818}, KEYWORDS = {Monotonicity}, } @article {Manherz69, AUTHOR = {Manherz, R. K.}, TITLE = {New energy theorems in {F}ourier transform theory}, JOURNAL = {Proc. IEEE}, VOLUME = {57}, YEAR = {1969}, PAGES = {826--827}, MRCLASS = {94A05}, MRNUMBER = {46 \#5028}, } @article {ManherzHakimi69, AUTHOR = {Manherz, R. K. and Hakimi, S. L.}, TITLE = {The generalized inverse in network analysis and quadratic error-minimization problems}, JOURNAL = {IEEE Trans. Circuit Theory}, VOLUME = {CT-16}, YEAR = {1969}, PAGES = {559--562}, MRCLASS = {15.15 (94.00)}, MRNUMBER = {42 \#284}, } @BOOK{Marcus73, author = {Marcus, M.}, title = {Finite {D}imensional {M}ultilinear {A}lgebra, {P}art 1}, publisher = {Marcel Dekker}, year = {1973}, address = {New York}, } @BOOK{Marcus75, author = {Marcus, M.}, title = {Finite {D}imensional {M}ultilinear {A}lgebra, {P}art 2}, publisher = {Marcel Dekker}, year = {1975}, address = {New York}, } @article {Marcus89, AUTHOR = {Marcus, M.}, TITLE = {A unified exposition of some classical matrix theorems}, JOURNAL = LINMA, VOLUME = {25}, YEAR = {1989}, PAGES = {137--147}, MRCLASS = {}, MRNUMBER = {}, } @BOOK{MarcusMinc64, author = {M. Marcus and H. Minc}, title = {A {S}urvey of {M}atrix {T}heory and {M}atrix {I}nequalities}, publisher = {Allyn \& Bacon}, year = {1964}, address = {Boston, Mass.}, } @article {Markham76, AUTHOR = {Markham, T. L.}, TITLE = {An application of theorems of {S}chur and {A}lbert}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {59}, YEAR = {1976}, NUMBER = {2}, PAGES = {205--210}, MRCLASS = {15A48 (15A57)}, MRNUMBER = {55 \#5668}, } @article {Markiewicz96, AUTHOR = {Markiewicz, A.}, TITLE = {Characterization of general ridge estimators}, JOURNAL = {Statist. Probab. Lett.}, FJOURNAL = {Statistics \& Probability Letters}, VOLUME = {27}, YEAR = {1996}, NUMBER = {2}, PAGES = {145--148}, ISSN = {0167-7152}, CODEN = {SPLTDC}, MRCLASS = {}, MRNUMBER = {98e:62105}, } @article {Markiewicz99, AUTHOR = {Markiewicz, A.}, TITLE = {Simultaneous polar decomposition of rectangular complex matrices}, JOURNAL = LINAA1, VOLUME = {289}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {279--284}, MRCLASS = {15A23}, MRNUMBER = {99m:15008}, KEYWORDS = {Polar decomposition, partial order}, NOTE = {(application of \cite{HaukeMarkiewicz95a})}, } @article{Marquardt70, author = {Marquardt, M. D.}, year = {1970}, title = {Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Regression}, journal = {Technometrics}, volume = {12}, pages = {591-613}, kwds = {stat, regr, nlop, ginv, ridge regression}, } @article {Marsaglia64, AUTHOR = {Marsaglia, G.}, TITLE = {Conditional means and variances of normal variables with singular convariance matrix}, JOURNAL = {J. Amer. Statist. Assoc.}, VOLUME = {58}, YEAR = {1964}, PAGES = {1203--1204}, } @article {MarsagliaStyan74, AUTHOR = {Marsaglia, G. and Styan, G. P. H.}, TITLE = {Equalities and inequalities for ranks of matrices}, JOURNAL = LINMA, VOLUME = {2}, YEAR = {1974/75}, PAGES = {269--292}, MRCLASS = {15A45}, MRNUMBER = {52 \#5711}, } @article {Marti78, AUTHOR = {Marti, J. T.}, TITLE = {An algorithm for computing minimum norm solutions of {F}redholm integral equations of the first kind}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {15}, YEAR = {1978}, NUMBER = {6}, PAGES = {1071--1076}, MRCLASS = {65R20}, MRNUMBER = {80b:65154}, NOTE = {(see \cite{HickeyLuecke82})}, } @ARTICLE{MartinEtAl66, author = {Martin, R. S. and Peters, G. and Wilkinson, J. H.}, title = {Iterative refinement of the solution of a positive definite system of equations}, journal = NUMEM, year = {1966}, volume = {8}, pages = {203--216}, NOTE = {(republished, pp. 31--44 in \cite{WilkinsonReinsch71})}, } @article {Martinez79, AUTHOR = {Mart{\'\i}nez, J. M.}, TITLE = {A bound for the {M}oore-{P}enrose pseudoinverse of a matrix}, JOURNAL = {Comment. Math. Univ. Carolin.}, FJOURNAL = {Commentationes Mathematicae Universitatis Carolinae}, VOLUME = {20}, YEAR = {1979}, NUMBER = {2}, PAGES = {357--360}, MRCLASS = {15A60 (15A09 65F20)}, MRNUMBER = {81j:15028}, } @article {Martinez-Torres00, AUTHOR = {Mart{\'\i}nez-Torres, E.}, TITLE = {Formulation of the vibrational theory in terms of redundant internal coordinates}, JOURNAL = {Journal of Molecular Structure}, VOLUME = {520}, YEAR = {2000}, PAGES = {53--61}, } @article {MathGenealogy, AUTHOR = {Mathematical Genealogy Project}, TITLE = {}, JOURNAL = {\verb+http:\\hcoonce.math.mankato.msus.edu/index.html+}, VOLUME = {}, YEAR = {}, PAGES = {}, } @article {MathewMitra84, AUTHOR = {Mathew, T. and Mitra, S. K.}, TITLE = {Shorted operators and the identification problem---the real case}, JOURNAL = {IEEE Trans. Circuits and Systems}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems}, VOLUME = {31}, YEAR = {1984}, NUMBER = {3}, PAGES = {299--300}, MRCLASS = {15A48 (93B30)}, MRNUMBER = {86c:15008}, } @BOOK{Maxwell1892, author = {Maxwell, J. C.}, title = {Treatise of {E}lectricity and {M}agnetism}, publisher = {Oxford University Press}, year = {1892}, volume = {I}, address = {Oxford}, edition = {3rd}, } @article {Mayne66, AUTHOR = {Mayne, D. Q.}, TITLE = {An algorithm for the calculation of the pseudo-inverse of a singular matrix}, JOURNAL = {Comput. J.}, VOLUME = {9}, YEAR = {1966}, PAGES = {312--317}, MRCLASS = {65.35}, MRNUMBER = {34 \#2167}, } @article {Mayne69, AUTHOR = {Mayne, D. Q.}, TITLE = {On the calculation of pseudoinverses}, JOURNAL = {IEEE Trans. Automatic Control}, VOLUME = {AC-14}, YEAR = {1969}, PAGES = {204--205}, MRCLASS = {15.15}, MRNUMBER = {39 \#4179}, } @article {Mbekhta95, AUTHOR = {Mbekhta, M.}, TITLE = {On the generalized resolvent in {B}anach spaces}, JOURNAL = JMATA, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {189}, YEAR = {1995}, NUMBER = {2}, PAGES = {362--377}, MRCLASS = {47A10 (47A53 47A56)}, MRNUMBER = {96f:47004}, } @article {MayorgaEtAl92, AUTHOR = {Mayorga, R. V. and Wong, A. K. C. and Milano, N.}, TITLE = {A fast procedure for manipulator inverse kinematics evaluation and pseudoinverse robustness}, JOURNAL = {IEEE Trans. Systems Man Cybernet.}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Systems, Man, and Cybernetics}, VOLUME = {22}, YEAR = {1992}, NUMBER = {4}, PAGES = {790--798}, MRCLASS = {70B15 (70-08)}, MRNUMBER = {93g:70005}, } @ARTICLE{McCoy39, author = {McCoy, N. H.}, title = {Generalized regular rings}, journal = BULAM1, year = {1939}, volume = {45}, pages = {175--178}, } @article {McDonald80, AUTHOR = {McDonald, G. C.}, TITLE = {Some algebraic properties of ridge coefficients}, JOURNAL = {J. Roy. Statist. Soc. B}, VOLUME = {42}, YEAR = {1980}, NUMBER = {1}, PAGES = {31--34}, MRCLASS = {}, MRNUMBER = {}, } @article {McMathSims80, AUTHOR = {McMath, J. S. and Sims, S. E.}, TITLE = {Mean value theorems for a matrix valued derivative}, JOURNAL = LINMA, VOLUME = {9}, YEAR = {1980/81}, NUMBER = {4}, PAGES = {255--261}, MRCLASS = {65F99 (15A45 26A24)}, MRNUMBER = {82j:65025}, } @article {McMathEtAl77, AUTHOR = {McMath, J. S. and Sims, S. E. and Hallum, C. R.}, TITLE = {On the properties of a matrix valued derivative utilizing the {M}oore-{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {18}, YEAR = {1977}, NUMBER = {3}, PAGES = {281--291}, MRCLASS = {65F20 (15A99)}, MRNUMBER = {58 \#8201}, NOTE = {(see \cite{McMathSims80})}, } @article {McMathEtAl80, AUTHOR = {McMath, J. S. and Sims, S. E. and Hallum, C. R.}, TITLE = {A comparison of various derivatives for matrix-valued functions}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \&\ Mathematics with Applications. An International Journal}, VOLUME = {6}, YEAR = {1980}, NUMBER = {2}, PAGES = {161--166}, MRCLASS = {65F99 (15A09 26E99)}, MRNUMBER = {82d:65043}, } @article {Meenakshi83, AUTHOR = {Meenakshi, A.}, TITLE = {On integral ${EP}\sb{r}$ matrices}, JOURNAL = {Period. Math. Hungar.}, FJOURNAL = {Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society}, VOLUME = {14}, YEAR = {1983}, NUMBER = {3-4}, PAGES = {229--234}, MRCLASS = {15A36 (15A09 15A57)}, MRNUMBER = {85d:15020}, } @article {MeenakshiAnandam92, AUTHOR = {Meenakshi, A. and Anandam, N.}, TITLE = {Polynomial generalized inverses of a partitioned polynomial matrix}, JOURNAL = {J. Indian Math. Soc. (N.S.)}, VOLUME = {58}, YEAR = {1992}, NUMBER = {1-4}, PAGES = {11--18}, MRCLASS = {15A09}, MRNUMBER = {94b:15001}, } @ARTICLE{Meicler68, author = {Meicler, M.}, title = {Chebyshev solution of an inconsistent system of $n+1$ linear equations in $n$ unknowns in terms of its least squares solution}, journal = SIAMR, year = {1968}, volume = {10}, pages = {373--375}, } @article {Meicler69, AUTHOR = {Meicler, M.}, TITLE = {A steepest ascent method for the {C}hebyshev problem}, JOURNAL = {Math. Comp.}, VOLUME = {23}, YEAR = {1969}, PAGES = {813--817}, MRCLASS = {65.30}, MRNUMBER = {41 \#2898}, } @article {MeisterSpeck85, AUTHOR = {Meister, E. and Speck, F. {-O}.}, TITLE = {The {M}oore-{P}enrose inverse of {W}iener-{H}opf operators on the half axis and the quarter plane}, JOURNAL = {J. Integral Equations}, VOLUME = {9}, YEAR = {1985}, NUMBER = {1}, PAGES = {45--61}, MRCLASS = {47B35 (45E10)}, MRNUMBER = {86h:47035}, } } @preamble{ "\def\cprime{$'$} " } @article {Meleshko76, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Statistical recurrent estimation based on pseudoinverse operators}, JOURNAL = {Avtomat. i Telemeh.}, FJOURNAL = {Avtomat. i Telemeh.}, YEAR = {1976}, NUMBER = {8}, PAGES = {101--110}, MRCLASS = {93E10}, MRNUMBER = {56 \#15050}, NOTE = {(English translation \textit{Automat. Remote Control} \textbf{37}(1976), no. 8, part 2, 1227--1235 (1977)}, } @article {Meleshko77, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Pseudoinverse operators in {B}anach spaces}, JOURNAL = {Ukrain. Mat. \v Z.}, VOLUME = {29}, YEAR = {1977}, NUMBER = {6}, PAGES = {738--749, 851}, MRCLASS = {47A50}, MRNUMBER = {58 \#17910}, NOTE = {English translation: \textit{Ukrainian Math. J.} \textbf{29} (1977), no. 6, 545--553}, } @article {Meleshko77a, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {A pseudo-inversion of closed operators that is stable under perturbations}, JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {17}, YEAR = {1977}, NUMBER = {5}, PAGES = {1132--1143, 1332}, MRCLASS = {47A55 (65J05)}, MRNUMBER = {58 \#17922}, } @article {Meleshko78, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Pseudoinverse operators, and the recursive calculation of pseudosolutions in {H}ilbert spaces}, JOURNAL = {Sibirsk. Mat. \v Z.}, VOLUME = {19}, YEAR = {1978}, NUMBER = {1}, PAGES = {108--121, 238}, MRCLASS = {47A50 (65J05)}, MRNUMBER = {58 \#7148}, NOTE = {(generalization of Greville's method to Hilbert space, see \cite{Greville60}. English translation: \textit{Siberian Math. J.} \textbf{19} (1978), no. 1, 75--85)}, } @article {Meleshko79, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Perturbations of unbounded closed pseudoinverse operators}, JOURNAL = {Differentsial\cprime nye Uravneniya}, FJOURNAL = {Differentsial\cprime nye Uravneniya}, VOLUME = {15}, YEAR = {1979}, NUMBER = {4}, PAGES = {681--694, 765}, ISSN = {0374-0641}, MRCLASS = {47A50 (47A05 47A53 47A55)}, MRNUMBER = {80m:47010}, NOTE = {English translation: Differential Equations 15 (1979), no. 4, 477--487 (1980)}, } @article {Meleshko79a, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {An investigation of stable ${L}$-pseudo-inverses of unbounded closed operators by the regularization method}, JOURNAL = {Differentsial\cprime nye Uravneniya}, FJOURNAL = {Differentsial\cprime nye Uravneniya}, VOLUME = {15}, YEAR = {1979}, NUMBER = {5}, PAGES = {921--935, 958--959}, MRCLASS = {47A50 (65J10)}, MRNUMBER = {80i:47020}, NOTE = {English translation: Differential Equations 15 (1979), no. 5, 653--664}, } @article {Meleshko79b, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Properties of pseudo-inverse operators in {B}anach spaces}, JOURNAL = {Dokl. Akad. Nauk SSSR}, FJOURNAL = {Doklady Akademii Nauk SSSR}, VOLUME = {249}, YEAR = {1979}, NUMBER = {5}, PAGES = {1055--1059}, ISSN = {0002-3264}, MRCLASS = {47A05 (47A50)}, MRNUMBER = {81a:47004}, MRREVIEWER = {C. Ilioi}, } @article {Meleshko80, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Filtering and identification of stochastic control systems using pseudoinverses}, JOURNAL = {Kibernetika (Kiev)}, FJOURNAL = {Otdelenie Matematiki, Mekhaniki i Kibernetiki Akademii Nauk Ukrainsko\u \i \ SSR. Kibernetika}, YEAR = {1980}, NUMBER = {5}, PAGES = {130--140}, MRCLASS = {93E11 (93E10)}, MRNUMBER = {84k:93068}, } @preamble{ "\def\cprime{$'$} " } @article {Meleshko81, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Perturbed iteration methods for determining ${L}$\ generalized solutions of nonlinear operator equations}, JOURNAL = {Differentsial\cprime nye Uravneniya}, FJOURNAL = {Differentsial\cprime nye Uravneniya}, VOLUME = {17}, YEAR = {1981}, NUMBER = {3}, PAGES = {541--557, 574--575}, ISSN = {0374-0641}, MRCLASS = {47H17 (65J15)}, MRNUMBER = {82i:47097}, NOTE = {(English translation: Differential Equations 17 (1981), no. 3, 377--390)}, } @article {Meleshko81a, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Algorithms of pseudoinverse operators for calculating generalized solutions of nonlinear equations. {I}}, JOURNAL = {Avtomat. Sistemy Upravleniya i Pribory Avtomat.}, FJOURNAL = {Avtomatizirovannye Sistemy Upravleniya i Pribory Avtomatiki}, NUMBER = {59}, YEAR = {1981}, PAGES = {45--51, ii--iii}, MRCLASS = {65H10}, MRNUMBER = {83c:65129}, NOTE = {(Newton method, see \cite{Meleshko81b})}, } } @article {Meleshko81b, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Algorithms of pseudoinverse operators for calculating generalized solutions of nonlinear equations. {I}{I}}, JOURNAL = {Avtomat. Sistemy Upravleniya i Pribory Avtomat.}, FJOURNAL = {Avtomatizirovannye Sistemy Upravleniya i Pribory Avtomatiki}, NUMBER = {60}, YEAR = {1981}, PAGES = {20--27}, ISSN = {0135-1710}, MRCLASS = {65H10}, MRNUMBER = {84i:65053}, NOTE = {(Newton method)}, } @incollection {Meleshko82, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Perturbation-resistant algorithms for pseudoinversion of rectangular matrices using the {L}agrange transform}, BOOKTITLE = {Mathematical {M}ethods of {C}ybernetics}, PAGES = {24--37}, PUBLISHER = {Akad. Nauk Ukrain. SSR Inst. Kibernet.}, ADDRESS = {Kiev}, YEAR = {1982}, MRCLASS = {65F20}, MRNUMBER = {84h:65041}, } @preamble{ "\def\cprime{$'$} " } @article {Meleshko85, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Regularized nonorthogonal factorizations and pseudoinversions of perturbed matrices}, JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.}, FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\ Matematiki i Matematichesko\u\i\ Fiziki}, VOLUME = {26}, YEAR = {1986}, NUMBER = {4}, PAGES = {485--498, 638}, MRCLASS = {15A23 (15A09)}, MRNUMBER = {87g:15016}, } @article {Meleshko90, AUTHOR = {Mele{\v{s}}ko, V. I.}, TITLE = {Accelerated regularized methods for calculating solutions of nonlinear nonregular equations}, JOURNAL = {Dokl. Akad. Nauk SSSR}, FJOURNAL = {Doklady Akademii Nauk SSSR}, VOLUME = {311}, YEAR = {1990}, NUMBER = {2}, PAGES = {282--287}, MRCLASS = {65J15 (47H17)}, MRNUMBER = {92a:65196}, NOTE = {(English translation: Soviet Math. Dokl. 41 (1990), no. 2, 246--251 (1991))}, } @article {MeleshkoZadachin87, AUTHOR = {Mele{\v{s}}ko, V. I. and Zadachin, V. M.}, TITLE = {Factorizations and pseudo-inversions of singular perturbed matrices with nonfixed signs}, JOURNAL = {Izv. Vyssh. Uchebn. Zaved. Mat.}, FJOURNAL = {Izvestiya Vysshikh Uchebnykh Zavedeni\u\i. Matematika}, YEAR = {1987}, NUMBER = {11}, PAGES = {42--50, 88}, ISSN = {0021-3446}, CODEN = {IVUMBY}, MRCLASS = {15A23 (15A09 15A60 47A68)}, MRNUMBER = {89a:15013}, NOTE = {(English translation: \textit{Soviet Math.} (Iz. VUZ) \textbf{31} (1987), no. 11, 53--62)}, } @article {Merz74, AUTHOR = {Merz, G.}, TITLE = {{\"U}ber die {I}nterpolationsaufgabe bei nat\"urlichen {P}olynom-{S}plines mit {\"a}quidistanten {K}noten}, JOURNAL = {J. Approximation Theory}, VOLUME = {10}, YEAR = {1974}, PAGES = {151--158}, MRCLASS = {41A15}, MRNUMBER = {50 \#2761}, } @article {Metcalf65, AUTHOR = {Metcalf, F. T.}, TITLE = {A {B}essel-{S}chwarz inequality for {G}ramians and related bounds for determinants}, JOURNAL = {Ann. Mat. Pura Appl. (4)}, VOLUME = {68}, YEAR = {1965}, PAGES = {201--232}, MRCLASS = {15.70 (15.58)}, MRNUMBER = {31 \#5874}, } @article {Meyer69a, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {On ranks of pseudoinverses}, JOURNAL = SIAMR, VOLUME = {11}, YEAR = {1969}, PAGES = {382--385}, MRCLASS = {15.15}, MRNUMBER = {40 \#5630}, } @article {Meyer69b, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {On the construction of solutions to the matrix equations ${A}{X}={A}$ and ${Y}{A}={A}$}, JOURNAL = SIAMR, VOLUME = {11}, YEAR = {1969}, PAGES = {612--615}, MRCLASS = {15.35}, MRNUMBER = {40 \#7284}, } @article {Meyer70a, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Generalized inverses of triangular matrices}, JOURNAL = SIAJA, VOLUME = {18}, YEAR = {1970}, PAGES = {401--406}, MRCLASS = {15.15}, MRNUMBER = {41 \#1754}, } @article {Meyer70b, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Some remarks on ${EP}\sb{r}$ matrices, and generalized inverses}, JOURNAL = LINAA1, VOLUME = {3}, YEAR = {1970}, PAGES = {275--278}, MRCLASS = {15.15}, MRNUMBER = {42 \#1837}, } @article {Meyer70c, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Generalized inverses of block triangular matrices}, JOURNAL = SIAJA, VOLUME = {19}, YEAR = {1970}, PAGES = {741--750}, MRCLASS = {15.15}, MRNUMBER = {42 \#7676}, } @article {Meyer71, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Representations for $(1)$- and $(1,\,2)$-inverses for partitioned matrices}, JOURNAL = LINAA1, VOLUME = {4}, YEAR = {1971}, PAGES = {221--232}, MRCLASS = {15.15}, MRNUMBER = {43 \#7439}, } @article {Meyer72, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {The {M}oore-{P}enrose inverse of a bordered matrix}, JOURNAL = LINAA1, VOLUME = {5}, YEAR = {1972}, PAGES = {375--382}, MRCLASS = {15A09}, MRNUMBER = {46 \#3522}, } @article {Meyer73a, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Generalized inversion of modified matrices}, JOURNAL = SIAJA, VOLUME = {24}, YEAR = {1973}, PAGES = {315--323}, MRCLASS = {15A09}, MRNUMBER = {47 \#5010}, } @article {Meyer73b, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Generalized inverses and ranks of block matrices}, JOURNAL = SIAJA, VOLUME = {25}, YEAR = {1973}, PAGES = {597--602}, MRCLASS = {15A09}, MRNUMBER = {48 \#8521}, } @article {Meyer74, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Limits and the index of a square matrix}, JOURNAL = SIAJA, VOLUME = {26}, YEAR = {1974}, PAGES = {469--478}, MRCLASS = {15A09}, MRNUMBER = {51 \#539}, NOTE = {(see \cite{Rothblum76})}, } @article {Meyer75a, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {The role of the group generalized inverse in the theory of finite {M}arkov chains}, JOURNAL = SIAMR, VOLUME = {17}, YEAR = {1975}, PAGES = {443--464}, MRCLASS = {60J10}, MRNUMBER = {52 \#4419}, KEYWORDS = {appmar, invgr}, } @inproceedings{Meyer82, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Analysis of finite {M}arkov chains by group inversion techniques}, CROSSREF = {Campbell82a}, PAGES = {50--81}, YEAR = {1982}, MRCLASS = {60J10 (15A09)}, MRNUMBER = {84b:60090}, KEYWORDS = {appmar, invgr}, } @incollection {Meyer93, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {The character of a finite {M}arkov chain}, BOOKTITLE = {Linear {A}lgebra, {M}arkov {C}hains, and {Q}ueueing {M}odels ({M}inneapolis, {MN}, 1992)}, PAGES = {47--58}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1993}, MRCLASS = {60J10 (15A51 65F15)}, MRNUMBER = {94h:60100}, KEYWORDS = {appmar}, } @book {Meyer00, AUTHOR = {Meyer, Jr., C. D.}, TITLE = {Matrix {A}nalysis and {A}pplied {L}inear {A}lgebra}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2000}, PAGES = {xii+718}, ISBN = {0-89871-454-0}, MRCLASS = {15-01}, MRNUMBER = {1 777 382}, } @article {MeyerPainter70, AUTHOR = {Meyer, Jr., C. D. and Painter, R. J.}, TITLE = {Note on a least squares inverse for a matrix}, JOURNAL = JASSC, VOLUME = {17}, YEAR = {1970}, PAGES = {110--112}, MRCLASS = {15.15}, MRNUMBER = {43 \#230}, } @article {MeyerPlemmons77, AUTHOR = {Meyer, Jr., C. D. and Plemmons, R. J.}, TITLE = {Convergent powers of a matrix with applications to iterative methods for singular linear systems}, JOURNAL = SIAJN, VOLUME = {14}, YEAR = {1977}, NUMBER = {4}, PAGES = {699--705}, MRCLASS = {65F20}, MRNUMBER = {56 \#4138}, } @article {MeyerRose77, AUTHOR = {Meyer, Jr., C. D. and Rose, N. J.}, TITLE = {The index and the {D}razin inverse of block triangular matrices}, JOURNAL = SIAJA, VOLUME = {33}, YEAR = {1977}, NUMBER = {1}, PAGES = {1--7}, MRCLASS = {15A09 (65F05)}, MRNUMBER = {57 \#345}, KEYWORDS = {strm, invD, indx}, } @article {MeyerShoaf80, AUTHOR = {Meyer, Jr., C. D. and Shoaf, J. M.}, TITLE = {Updating finite {M}arkov chains by using techniques of group matrix inversion}, JOURNAL = {J. Statist. Comput. Simulation}, FJOURNAL = {Journal of Statistical Computation and Simulation}, VOLUME = {11}, YEAR = {1980}, NUMBER = {3-4}, PAGES = {163--181}, MRCLASS = {60J10 (15A09)}, MRNUMBER = {82d:60122}, } @article {MeyerStadelmaier78, AUTHOR = {Meyer, Jr., C. D. and Stadelmaier, M. W.}, TITLE = {Singular ${M}$-matrices and inverse positivity}, JOURNAL = LINAA1, VOLUME = {22}, YEAR = {1978}, PAGES = {139--156}, MRCLASS = {15A09}, MRNUMBER = {80b:15008}, } @article {MeyerStewart88, AUTHOR = {Meyer, Jr., C. D. and Stewart, G. W.}, TITLE = {Derivatives and perturbations of eigenvectors}, JOURNAL = SIAJN, VOLUME = {25}, YEAR = {1988}, NUMBER = {3}, PAGES = {679--691}, MRCLASS = {65F15 (15A22 60J10)}, MRNUMBER = {89g:65043}, } @ARTICLE{Miao88, AUTHOR = {Miao, Jian Ming}, TITLE = {The weighted {M}oore-{P}enrose inverse of a rank-one modified matrix (Chinese)}, JOURNAL = {J. Shanghai Teachers University}, FJOURNAL = {Journal of Shanghai Teachers University. Natural Sciences}, VOLUME = {17}, YEAR = {1988}, NUMBER = {3}, PAGES = {21--26}, MRCLASS = {15A09}, MRNUMBER = {} } @article {Miao89, AUTHOR = {Miao, Jian Ming}, TITLE = {Representations for the weighted {M}oore-{P}enrose inverse of a partitioned matrix}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications}, VOLUME = {7}, YEAR = {1989}, NUMBER = {4}, PAGES = {321--323}, MRCLASS = {15A09}, MRNUMBER = {1 149 699}, } @article {Miao89a, AUTHOR = {Miao, Jian Ming}, TITLE = {The {M}oore-{P}enrose inverse of a rank-$r$ modified matrix}, JOURNAL = {Numer. Math. J. Chinese Univ.}, FJOURNAL = {Numerical Mathematics. A Journal of Chinese Universities. Gaodeng Xuexiao Jisuan Shuxue Xuebao}, VOLUME = {11}, YEAR = {1989}, NUMBER = {4}, PAGES = {355--361}, MRCLASS = {15A09}, MRNUMBER = {91a:15003}, } @ARTICLE{Miao89b, AUTHOR = {Miao, Jian Ming}, TITLE = {Some results on the {D}razin inverses for partitioned matrices ({C}hinese)}, JOURNAL = {J. Shanghai Teachers University}, FJOURNAL = {Journal of Shanghai Teachers University. Natural Sciences}, VOLUME = {18}, YEAR = {1989}, NUMBER = {2}, PAGES = {25--31}, MRCLASS = {15A09}, MRNUMBER = {92d:15005} } @ARTICLE{Miao89c, AUTHOR = {Miao, Jian Ming}, TITLE = {Representations for the weighted {M}oore-{P}enrose inverse of sums of matrices ({C}hinese)}, JOURNAL = {Comm. Appl. Math. and Comput.}, FJOURNAL = {Communication on Applied Mathematics and Computation}, VOLUME = {3}, YEAR = {1989}, NUMBER = {2}, PAGES = {83--86}, MRCLASS = {15A09}, MRNUMBER = {1 091 143} } @ARTICLE{Miao90, AUTHOR = {Miao, Jian Ming}, TITLE = {The {D}razin inverse of {H}essenberg matrices}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics}, VOLUME = {8}, YEAR = {1990}, NUMBER = {1}, PAGES = {23--29}, MRCLASS = {15A09}, MRNUMBER = {} } @article {Miao91, AUTHOR = {Miao, Jian Ming}, TITLE = {General expressions for the {M}oore-{P}enrose inverse of a $2\times 2$ block matrix}, JOURNAL = LINAA1, VOLUME = {151}, YEAR = {1991}, PAGES = {1--15}, MRCLASS = {15A09}, MRNUMBER = {92c:15005}, } @ARTICLE{Miao93, AUTHOR = {Miao, Jian Ming}, TITLE = {Reflexive generalized inverses and their minors}, JOURNAL = {Linear and Multilinear Algebra}, VOLUME = {35}, YEAR = {1993}, NUMBER = {2}, PAGES = {153--163}, MRCLASS = {15A09}, MRNUMBER = {95h:15007} } @article {MiaoBen-Israel92, AUTHOR = {Miao, Jian Ming and Ben-Israel, A.}, TITLE = {On principal angles between subspaces in ${R}\sp n$}, JOURNAL = LINAA1, VOLUME = {171}, YEAR = {1992}, PAGES = {81--98}, MRCLASS = {15A45 (15A15 15A18 15A57)}, MRNUMBER = {93i:15028}, } @article {MiaoBen-Israel93, AUTHOR = {Miao, Jian Ming and Ben-Israel, A.}, TITLE = {Minors of the {M}oore--{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {195}, YEAR = {1993}, PAGES = {191--207}, MRCLASS = {15A15 (15A09 15A57)}, MRNUMBER = {95g:15007}, KEYWORDS = {det, invMP}, } @article {MiaoBen-Israel94, AUTHOR = {Miao, Jian Ming and Ben-Israel, A.}, TITLE = {On $l\sb p$-approximate solutions of linear equations}, JOURNAL = LINAA1, VOLUME = {199}, YEAR = {1994}, PAGES = {305--327}, MRCLASS = {65F20}, MRNUMBER = {95c:65065}, KEYWORDS = {aprx, norm1, normC}, } @article {MiaoBen-Israel95, AUTHOR = {Miao, Jian Ming and Ben-Israel, A.}, TITLE = {The geometry of basic, approximate, and minimum-norm solutions of linear equations}, JOURNAL = LINAA1, VOLUME = {216}, YEAR = {1995}, PAGES = {25--41}, MRCLASS = {15A06 (65F20 90C08)}, MRNUMBER = {96e:15003}, } @article {MiaoBen-Israel96, AUTHOR = {Miao, Jian Ming and Ben-Israel, A.}, TITLE = {Product cosines of angles between subspaces}, JOURNAL = LINAA1, VOLUME = {237/238}, YEAR = {1996}, PAGES = {71--81}, MRCLASS = {15A03 (15A09)}, MRNUMBER = {97d:15002}, } @article {MiaoRobinson88, AUTHOR = {Miao, Jian Ming and Robinson, D. W.}, TITLE = {Group and {M}oore--{P}enrose inverses of regular morphisms with kernel and cokernel}, JOURNAL = LINAA1, VOLUME = {110}, YEAR = {1988}, PAGES = {263--270}, MRCLASS = {15A09 (18B99)}, MRNUMBER = {89h:15009}, } @article {MieheSchroder01, AUTHOR = {Miehe, C. and Schr{\"o}der, J.}, TITLE = {Comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity}, JOURNAL = {Internat. J. Numer. Methods Engrg.}, FJOURNAL = {International Journal for Numerical Methods in Engineering}, VOLUME = {50}, YEAR = {2001}, PAGES = {273--298}, } @article {Mihalyffy70, AUTHOR = {Mih{\'a}lyffy, L.}, TITLE = {A note on the matrix inversion by the partitioning technique}, JOURNAL = {Studia Sci. Math. Hungar.}, VOLUME = {5}, YEAR = {1970}, PAGES = {127--135}, MRCLASS = {65.35}, MRNUMBER = {42 \#5435}, } @ARTICLE{Mihalyffy71, author = {Mih{\'a}lyffy, L.}, title = {An alternative representation of the generalized inverse of partitioned matrices}, journal = LINAA1, year = {1971}, volume = {4}, pages = {95--100}, } @article {MillerCornuelle99, AUTHOR = {Miller, A. J. and Cornuelle, B. D.}, TITLE = {Forecasts from fits of frontal fluctuations}, JOURNAL = {Dynamics of Atmospheres and Oceans}, VOLUME = {29}, YEAR = {1999}, NUMBER = {2--4}, PAGES = {305--333}, } @article {MillikenAkdeniz77, AUTHOR = {Milliken, G. A. and Akdeniz, F.}, TITLE = {A theorem on the difference of the generalized inverses of two nonnegative matrices}, JOURNAL = {Comm. Statist.---Theory Methods}, VOLUME = {A6}, YEAR = {1977}, NUMBER = {1}, PAGES = {73--79}, MRCLASS = {15A48 (62J10)}, MRNUMBER = {56 \#390}, } @ARTICLE{Milne68, author = {Milne, R. D.}, title = {An oblique matrix pseudoinverse}, journal = SIAJA, year = {1968}, volume = {16}, pages = {931--944}, NOTE = {(see \cite{WardEtAl71})}, } @INPROCEEDINGS{MilnesEtAl68, author = {Milnes, H. W. and Amburgey, J. and Lewis, T. O. and Boullion, T. L.}, crossref = {BoullionOdell68}, title = {Spectral eigenvalue property of ${A}\sp{+}$ for rectangular matrices}, year = {1968}, pages = {98--113}, } @TECHREPORT{MinamideNakamura69, author = {Minamide, N. and Nakamura, K.}, title = {Minimum error control problem in Banach space}, institution = {Nagoya University}, year = {1969}, type = {Research Report of Automatic Control Lab}, number = {16}, address = {Nagoya, Japan}, } @ARTICLE{MinamideNakamura70, author = {Minamide, N. and Nakamura, K.}, title = {A restricted pseudoinverse and its applications to constrained minima}, journal = SIAJA, year = {1970}, volume = {19}, pages = {167--177}, } @ARTICLE{Mirsky60, author = {Mirsky, L.}, title = {Symmetric gauge functions and unitarily invariant norms}, journal = {Quart. J. Math. Oxford}, year = {1960}, volume = {11}, pages = {50--59}, } @ARTICLE{Mitra68, author = {Mitra, S. K.}, title = {On a generalized inverse of a matrix and applications}, journal = SANKA, year = {1968}, volume = {30}, pages = {107--114}, } @ARTICLE{Mitra68a, author = {Mitra, S. K.}, title = {A new class of g--inverse of square matrices}, journal = SANKA, year = {1968}, volume = {30}, pages = {323--330}, } @ARTICLE{Mitra72, author = {Mitra, S. K.}, title = {Fixed rank solutions of linear matrix equations}, journal = SANKA, year = {1972}, volume = {35}, pages = {387--392}, } @ARTICLE{Mitra73, author = {Mitra, S. K.}, title = {Common solutions to a pair of linear matrix equations ${A_1 XB_1=C_1,\,A_2 XB_2=C_2}$}, journal = PROCPS, year = {1973}, volume = {74}, pages = {213--216}, } @article {Mitra82, AUTHOR = {Mitra, S. K.}, TITLE = {Shorted operators and the identification problem}, JOURNAL = {IEEE Trans. Circuits and Systems}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems}, VOLUME = {29}, YEAR = {1982}, NUMBER = {8}, PAGES = {581--583}, MRCLASS = {15A57 (15A09 15A15)}, MRNUMBER = {84g:15027}, } @article {Mitra82a, AUTHOR = {Mitra, S. K.}, TITLE = {Simultaneous diagonalization of rectangular matrices}, JOURNAL = LINAA1, VOLUME = {47}, YEAR = {1982}, PAGES = {139--150}, MRCLASS = {}, MRNUMBER = {}, } @article {Mitra86, AUTHOR = {Mitra, S. K.}, TITLE = {The minus partial order and the shorted matrix}, JOURNAL = LINAA1, VOLUME = {83}, YEAR = {1986}, PAGES = {1--27}, MRCLASS = {}, MRNUMBER = {}, } @article {Mitra87, AUTHOR = {Mitra, S. K.}, TITLE = {On group inverses and the sharp order}, JOURNAL = LINAA1, VOLUME = {92}, YEAR = {1987}, PAGES = {17--37}, MRCLASS = {}, MRNUMBER = {}, } @incollection{Mitra89, AUTHOR = {Mitra, S. K.}, TITLE = {Block independence in generalized inverses: {A} coordinate free look}, BOOKTITLE = {Statistical {D}ata {A}nalysis and {I}nference (Y. Dodge, ed.)}, PAGES = {429--443}, PUBLISHER = {North Holland}, ADDRESS = {Amsterdam}, YEAR = {1989}, MRCLASS = {}, MRNUMBER = {}, } @article {Mitra90, AUTHOR = {Mitra, S. K.}, TITLE = {Shorted matrices in star and related orderings}, JOURNAL = {Circuits Systems Signal Process.}, FJOURNAL = {Circuits, Systems, and Signal Processing}, VOLUME = {9}, YEAR = {1990}, NUMBER = {2}, PAGES = {197--212}, MRCLASS = {94C05 (15A99 47A63)}, MRNUMBER = {91m:94039}, } @article {Mitra91, AUTHOR = {Mitra, S. K.}, TITLE = {Matrix partial order through generalized inverses: unified theory}, JOURNAL = LINAA1, VOLUME = {148}, YEAR = {1991}, PAGES = {237--263}, MRCLASS = {15A09}, MRNUMBER = {92e:15011}, } @article {Mitra94, AUTHOR = {Mitra, S. K.}, TITLE = {Separation theorems}, JOURNAL = LINAA1, VOLUME = {208/209}, YEAR = {1994}, PAGES = {239--256}, MRCLASS = {15A09 (15A24 15A99)}, MRNUMBER = {95e:15004}, } @article {Mitra97, AUTHOR = {Mitra, S. K.}, TITLE = {Erratum: ``{T}he nonunique shorted matrix'' [{L}inear {A}lgebra {A}ppl.\ {\bf 237/238} (1996), 41--70; {M}{R} 97a:15012] by {M}itra and {K}. {M}. {P}rasad}, JOURNAL = LINAA1, VOLUME = {260}, YEAR = {1997}, PAGES = {323}, MRCLASS = {15A09 (15A45 47A63)}, MRNUMBER = {1 448 364}, } @article {Mitra99, AUTHOR = {Mitra, S. K.}, TITLE = {Diagrammatic presentation of inner and outer inverses: ${S}$-diagrams}, JOURNAL = LINAA1, VOLUME = {287}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {271--288}, MRCLASS = {15A09}, MRNUMBER = {2000b:15002}, } @article {MitraBhimasankaram71, AUTHOR = {Mitra, S. K. and Bhimasankaram, P.}, TITLE = {Generalized inverses of partitioned matrices and recalculation of least squares estimates for data or model changes}, JOURNAL = {Sankhy\=a Ser. A}, VOLUME = {33}, YEAR = {1971}, PAGES = {395--410}, MRCLASS = {62J05 (15A09)}, MRNUMBER = {47 \#2760}, } @article {MitraHartwig92, AUTHOR = {Mitra, S. K. and Hartwig, R. E.}, TITLE = {Partial orders based on outer inverses}, JOURNAL = LINAA1, VOLUME = {176}, YEAR = {1992}, PAGES = {3--20}, MRCLASS = {15A09 (15A06 15A24)}, MRNUMBER = {93m:15008}, } @article {MitraOdell86, AUTHOR = {Mitra, S. K. and Odell, P. L.}, TITLE = {On parallel summability of matrices}, JOURNAL = LINAA1, VOLUME = {74}, YEAR = {1986}, PAGES = {239--255}, MRCLASS = {15A48}, MRNUMBER = {87d:15014}, } @article {MitraPrasad96, AUTHOR = {Mitra, S. K. and Prasad, K. M.}, TITLE = {The nonunique shorted matrix}, JOURNAL = LINAA1, VOLUME = {237/238}, YEAR = {1996}, PAGES = {41--70}, MRCLASS = {15A09 (15A45 47A63)}, MRNUMBER = {97a:15012}, NOTE = {(erratum in \cite{Mitra97})}, } @article {MitraPrasad97a, AUTHOR = {Mitra, S. K. and Prasad, K. M.}, TITLE = {The nonunique parallel sum}, JOURNAL = LINAA1, VOLUME = {259}, YEAR = {1997}, PAGES = {77--99}, MRCLASS = {15A30 (15A09 47A63)}, MRNUMBER = {98g:15023}, } @article {MitraPuri79, AUTHOR = {Mitra, S. K. and Puri, M. L.}, TITLE = {Shorted operators and generalized inverses of matrices}, JOURNAL = LINAA1, VOLUME = {25}, YEAR = {1979}, PAGES = {45--56}, MRCLASS = {15A09}, MRNUMBER = {80b:15009}, } @article {MitraPuri82, AUTHOR = {Mitra, S. K. and Puri, M. L.}, TITLE = {Shorted matrices---an extended concept and some applications}, JOURNAL = LINAA1, VOLUME = {42}, YEAR = {1982}, PAGES = {57--79}, MRCLASS = {15A04 (15A24 94C05)}, MRNUMBER = {83e:15003}, } @article {MitraPuri83, AUTHOR = {Mitra, S. K. and Puri, M. L.}, TITLE = {The fundamental bordered matrix of linear estimation and the {D}uffin-{M}orley general linear electromechanical systems}, JOURNAL = {Applicable Anal.}, FJOURNAL = {Applicable Analysis. An International Journal}, VOLUME = {14}, YEAR = {1983}, NUMBER = {4}, PAGES = {241--258}, MRCLASS = {15A09 (15A99)}, MRNUMBER = {84f:15009}, } @ARTICLE{MitraRao68, author = {Mitra, S. K. and Rao, C. R.}, title = {Some results in estimation and tests of linear hypotheses under the {G}auss--{M}arkov model}, journal = SANKA, year = {1968}, volume = {30}, pages = {281--290}, } @ARTICLE{MitraRao69, author = {Mitra, S. K. and Rao, C. R.}, title = {Conditions for optimality and validity of simple least squares theory}, journal = {Ann. Math. Statist.}, year = {1969}, volume = {40}, pages = {1617--1624}, } @article {MitraRao74, AUTHOR = {Mitra, S. K. and Rao, C. R.}, TITLE = {Projections under seminorms and generalized {M}oore {P}enrose inverses}, JOURNAL = LINAA1, VOLUME = {9}, YEAR = {1974}, PAGES = {155--167}, MRCLASS = {15A60}, MRNUMBER = {50 \#4635}, } @article {MizelRao62, AUTHOR = {Mizel, V. J. and Rao, M. M.}, TITLE = {Nonsymmetric projections in {H}ilbert space}, JOURNAL = {Pacific J. Math.}, VOLUME = {12}, YEAR = {1962}, PAGES = {343--357}, MRCLASS = {47.40}, MRNUMBER = {25 \#4365}, } @article {MohanEtAl84, AUTHOR = {Mohan, S. R. and Neumann, M. and Ramamurthy, K. G.}, TITLE = {Nonnegativity of principal minors of generalized inverses of $M$-matrices}, JOURNAL = LINAA1, VOLUME = {58}, YEAR = {1984}, PAGES = {247--259}, MRCLASS = {}, MRNUMBER = {}, } @article {MohideenCherkassky91, AUTHOR = {Mohideen, S. and Cherkassky, V.}, TITLE = {On recursive calculation of the generalized inverse of a matrix}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {17}, YEAR = {1991}, NUMBER = {1}, PAGES = {130--147}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {92c:65042}, } @article {MohsenStoer01, AUTHOR = {Mohsen, A. and Stoer, J.}, TITLE = {A variable metric method for approximating generalized inverses of matrices}, JOURNAL = {ZAMM Z. Angew. Math. Mech.}, FJOURNAL = {ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics}, VOLUME = {81}, YEAR = {2001}, NUMBER = {7}, PAGES = {435--446}, MRCLASS = {65F20 (65F10)}, MRNUMBER = {2002e:65062}, } @incollection {MolchanovGalba80, AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.}, TITLE = {Generalized difference {G}reen functions and elements of pseudoinverse matrices}, BOOKTITLE = {Questions on {N}umerical {M}athematics}, PAGES = {27--33, 40}, PUBLISHER = {Akad. Nauk Ukrain. SSR Inst. Kibernet.}, ADDRESS = {Kiev}, YEAR = {1980}, MRCLASS = {65N99 (65F20)}, MRNUMBER = {82m:65111}, } @article {MolchanovGalba82, AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.}, TITLE = {Difference methods for elliptic partial differential equations with nonunique solutions}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {19}, YEAR = {1982}, NUMBER = {3}, PAGES = {531--547}, MRCLASS = {65N05}, MRNUMBER = {83e:65160}, KEYWORDS = {Discrete Green function}, } @article {MolchanovGalba83, AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.}, TITLE = {A weighted pseudoinverse for complex matrices}, JOURNAL = {Ukrain. Mat. Zh.}, FJOURNAL = {Akademiya Nauk Ukrainsko\u \i \ SSR. Institut Matematiki. Ukrainski\u \i \ Matematicheski\u \i \ Zhurnal}, VOLUME = {35}, YEAR = {1983}, NUMBER = {1}, PAGES = {53--57, 134}, MRCLASS = {15A09 (65F20)}, MRNUMBER = {84e:15004}, } @article {MolchanovGalba89, AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.}, TITLE = {Weighted pseudo-inversion of matrices with positive-definite weights}, JOURNAL = {Dokl. Akad. Nauk Ukrain. SSR Ser. A}, FJOURNAL = {Akademiya Nauk Ukrainsko\u\i\ SSR. Doklady. Seriya A. Fiziko-Matematicheskie i Tekhnicheskie Nauki}, YEAR = {1989}, NUMBER = {7}, PAGES = {15--17, 85}, MRCLASS = {15A09 (15A06 65F05 65F10)}, MRNUMBER = {90j:15011}, } @ARTICLE{Moler67, author = {Moler, C. B.}, title = {Iterative refinement in floating point}, journal = JASSC, year = {1967}, volume = {14}, pages = {316--321}, } @article {MolerVanLoan78, AUTHOR = {Moler, C. B. and Van Loan, C. F.}, TITLE = {Nineteen dubious ways to compute the exponential of a matrix}, JOURNAL = SIAMR, VOLUME = {20}, YEAR = {1978}, NUMBER = {}, PAGES = {801--836}, MRCLASS = {}, MRNUMBER = {}, } @article {Monch78, AUTHOR = {M{\"o}nch, W.}, TITLE = {Monotone {E}inschliessung der {M}oore-{P}enrose {P}seudoinversen einer {M}atrix}, JOURNAL = {Z. Angew. Math. Mech.}, VOLUME = {58}, YEAR = {1978}, NUMBER = {2}, PAGES = {67--74}, MRCLASS = {65F20}, MRNUMBER = {57 \#18056}, } @article {Monch82, AUTHOR = {M{\"o}nch, W.}, TITLE = {Iterative refinement of approximations to a generalized inverse of a matrix}, JOURNAL = {Computing}, FJOURNAL = {Computing. Archiv f\"ur Informatik und Numerik}, VOLUME = {28}, YEAR = {1982}, NUMBER = {1}, PAGES = {79--87}, ISSN = {0010-485X}, CODEN = {CMPTA2}, MRCLASS = {65-04 (15A09 65F20)}, MRNUMBER = {83a:65001}, } @ARTICLE{Mond69, author = {Mond, B.}, title = {Generalized inverse extensions of matrix inequalities}, journal = LINAA1, year = {1969}, volume = {2}, pages = {393--399}, } @article {MondPecaric93, AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.}, TITLE = {Inequalities with weights for powers of generalised inverses}, JOURNAL = {Bull. Austral. Math. Soc.}, FJOURNAL = {Bulletin of the Australian Mathematical Society}, VOLUME = {48}, YEAR = {1993}, NUMBER = {1}, PAGES = {7--12}, MRCLASS = {15A09 (15A45)}, MRNUMBER = {94d:15002}, } @article {MondPecaric94, AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.}, TITLE = {Inequalities with weights for powers of generalized inverses. {I}{I}}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {210}, YEAR = {1994}, PAGES = {265--272}, MRCLASS = {15A45 (15A09 15A48)}, MRNUMBER = {95h:15031}, } @article {MondPecaric96, AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.}, TITLE = {On matrix convexity of the {M}oore-{P}enrose inverse}, JOURNAL = {Internat. J. Math. Math. Sci.}, VOLUME = {19}, YEAR = {1996}, NUMBER = {4}, PAGES = {707--710}, MRCLASS = {15A09 (15A45)}, MRNUMBER = {97d:15007}, KEYWORDS = {matpsd, ineq, invMP}, } @article {MondPecaric98, AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.}, TITLE = {Hadamard products and generalized inverses}, JOURNAL = {Austral. Math. Soc. Gaz.}, FJOURNAL = {The Australian Mathematical Society. Gazette}, VOLUME = {25}, YEAR = {1998}, NUMBER = {4}, PAGES = {194--197}, MRCLASS = {15A09}, MRNUMBER = {99k:15006}, } @incollection{Moore09, AUTHOR = {Moore, E. H.}, TITLE = {On a form of general analysis with applications to linear differential equations and integral equations}, BOOKTITLE = {Atti del IV Congresso Internazionale dei Matematici (Rome 1908). Vol 2}, PAGES = {98--114}, PUBLISHER = {}, ADDRESS = {Roma}, YEAR = {1909}, MRCLASS = {}, MRNUMBER = {}, } @incollection{Moore10, AUTHOR = {Moore, E. H.}, TITLE = {Introduction to a {F}orm of {G}eneral {A}nalysis}, BOOKTITLE = {The New Haven Mathematical Colloquium}, PAGES = {1--150}, PUBLISHER = {Yale University Press}, ADDRESS = {New Haven, CT}, YEAR = {1910}, NOTE = {(see review in \cite{Birkhoff11})}, } @article{Moore12, author = {Moore, E. H.}, year = {1912}, title = {On the foundations of the theory of linear integral equations}, journal = TRAAM, volume = {18}, pages = {334-362}, KEYWORDS = {History, Moore, integral equations}, } @incollection{Moore12a, AUTHOR = {Moore, E. H.}, TITLE = {On the fundamental functional operation of a general theory of linear integral equations}, BOOKTITLE = {Proceedings of the 5th {I}nternational {C}ongress of {M}athematicians}, PAGES = {230--255}, PUBLISHER = {}, ADDRESS = {Cambridge}, YEAR = {1912}, } @article{Moore15, author = {Moore, E. H.}, year = {1915}, title = {Definition of limit in general integral analysis}, journal = {Proc. Nat. Acad. Sci.}, volume = {1}, pages = {628}, } @article{Moore16, author = {Moore, E. H.}, year = {1916}, title = {On properly positive {H}ermitian matrices}, journal = BULAM1, volume = {23}, pages = {59}, KEYWORDS = {reproducing kernels}, } @article{Moore20, author = {Moore, E. H.}, year = {1920}, title = {On the Reciprocal of the General Algebraic Matrix}, journal = BULAM1, volume = {26}, pages = {394-395}, note = {(Abstract)}, KEYWORDS = {History, Moore-Penrose inverse, determinantal representation}, } @book{Moore35, author = {Moore, E. H. and Barnard, R. W.}, year = {1935}, title = {General {A}nalysis}, series = {Memoirs of the American Philosophical Society, I}, publisher = {American Philosophical Society}, address = {Philadelphia, Pennsylvania}, note = {(see specially Part 1, pp. 197--209)}, KEYWORDS = {book, alglin, his, ginv}, } @article{MooreSmith22, author = {Moore, E. H. and Smith, H. L.}, year = {1922}, title = {A general theory of limits}, journal = {Amer. J. Math.}, volume = {44}, pages = {102--121}, } @incollection {MooreNashed73, AUTHOR = {Moore, R. H. and Nashed, M. Z.}, TITLE = {Approximations of generalized inverses of linear operators in {B}anach spaces}, BOOKTITLE = {Approximation {T}heory ({P}roc. {I}nternat. {S}ympos., {U}niv. {T}exas, {A}ustin, {TX}, 1973)}, PAGES = {425--428}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1973}, MRCLASS = {47A55}, MRNUMBER = {48 \#9429}, } @article {MooreNashed74, AUTHOR = {Moore, R. H. and Nashed, M. Z.}, TITLE = {Approximations to generalized inverses of linear operators}, JOURNAL = SIAJA, VOLUME = {27}, YEAR = {1974}, PAGES = {1--16}, MRCLASS = {47A55 (65J05)}, MRNUMBER = {50 \#14301}, KEYWORDS = {invMP, pert, spacB, linop}, } @article {Moppert59, AUTHOR = {Moppert, C. F.}, TITLE = {On the {G}ram determinant}, JOURNAL = {Quart. J. Math. Oxford Ser. (2)}, VOLUME = {10}, YEAR = {1959}, PAGES = {161--164}, MRCLASS = {46.00 (15.00)}, MRNUMBER = {22 \#176}, } @article {Morley79a, AUTHOR = {Morley, T. D.}, TITLE = {Parallel summation, {M}axwell's principle and the infimum of projections}, JOURNAL = JMATA, VOLUME = {70}, YEAR = {1979}, NUMBER = {1}, PAGES = {33--41}, MRCLASS = {94C05 (47B15)}, MRNUMBER = {80g:94075}, KEYWORDS = {apphys, appnet, matpsd, proj, parsum}, } @article {Morley79b, AUTHOR = {Morley, T. D.}, TITLE = {A {G}auss-{M}arkov theorem for infinite-dimensional regression models with possibly singular covariance}, JOURNAL = SIAJA, VOLUME = {37}, YEAR = {1979}, NUMBER = {2}, PAGES = {257--260}, MRCLASS = {62J05}, KEYWORDS = {GauMar, spacH, inv1}, MRNUMBER = {80m:62069}, } @article {Morley89, AUTHOR = {Morley, T. D.}, TITLE = {An alternative approach to the parallel sum}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {10}, YEAR = {1989}, NUMBER = {3}, PAGES = {358--369}, MRCLASS = {47A63 (15A04)}, MRNUMBER = {91f:47026}, } @article {Morozov68, AUTHOR = {Morozov, V. A.}, TITLE = {The principle of disparity in solving operator equations by the method of regularization}, JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {8}, YEAR = {1968}, PAGES = {295--309}, MRCLASS = {65.50 (47.00)}, MRNUMBER = {39 \#5059}, } @article {Morozov69, AUTHOR = {Morozov, V. A.}, TITLE = {Pseudosolutions}, JOURNAL = {\u Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {9}, YEAR = {1969}, PAGES = {1387--1391}, MRCLASS = {47.10 (65.00)}, MRNUMBER = {41 \#9021}, } @article {Morozov70, AUTHOR = {Morozov, V. A.}, TITLE = {The optimal regularization of operator equations}, JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {10}, YEAR = {1970}, PAGES = {818--829}, MRCLASS = {47A50 (65J05)}, MRNUMBER = {46 \#690}, } @article {Morozov71, AUTHOR = {Morozov, V. A.}, TITLE = {An effective numerical algorithm for constructing pseudosolutions}, JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, VOLUME = {11}, YEAR = {1971}, PAGES = {260--262}, MRCLASS = {47.10 (65.00)}, MRNUMBER = {44 \#2056}, } @book {Morozov84, AUTHOR = {Morozov, V. A.}, TITLE = {Methods for {S}olving {I}ncorrectly {P}osed {P}roblems}, NOTE = {Translated from the Russian by A. B. Aries, Translation edited by Z. Nashed}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1984}, PAGES = {xviii+257}, ISBN = {0-387-096059-}, MRCLASS = {65-02 (47A50 47H17 65J05 65P05)}, MRNUMBER = {86d:65005}, } @ARTICLE{MorrisOdell68, author = {Morris, G. L. and Odell, P. L.}, title = {Common solutions for $n$ matrix equations with applications}, journal = JASSC, year = {1968}, volume = {15}, pages = {272--274}, } @article {MorrisOdell68a, AUTHOR = {Morris, G. L. and Odell, P. L.}, TITLE = {A characterization for generalized inverses of matrices}, JOURNAL = {SIAM Rev.}, VOLUME = {10}, YEAR = {1968}, PAGES = {208--211}, MRCLASS = {15.15}, MRNUMBER = {39 \#5593}, } @book{MostowSampson69, author = {Mostow, G. D. and Sampson, J. H.}, year = {1969}, title = {Linear {A}lgebra}, publisher = {McGraw--Hill}, address = {New York}, KEYWORDS = {book, algebra}, } @book{MostowEtAl63, author = {Mostow, G. D. and Sampson, J. H. and Meyer, J. {-P}.}, year = {1963}, title = {Fundamental {S}tructures of {A}lgebra}, publisher = {McGraw--Hill}, address = {New York}, KEYWORDS = {book, algebra}, } @article {MouraKitney91, AUTHOR = {Moura, L. and Kitney, R.}, TITLE = {A direct method for least-squares circle fitting}, JOURNAL = {Comput. Phys. Comm.}, FJOURNAL = {Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry}, VOLUME = {64}, YEAR = {1991}, NUMBER = {1}, PAGES = {57--63}, MRCLASS = {65D10 (62J10)}, MRNUMBER = {92a:65052}, NOTE = {(see \cite{Nievergelt94a})}, } @BOOK{Muller66, author = {M{\"u}ller, C.}, title = {Spherical {H}armonics}, publisher = {Springer-Verlag}, series = {Lecture Notes in Mathematics, No. 17}, year = {1966}, address = {New York}, } @ARTICLE{Munn61, author = {Munn, W. D.}, title = {Pseudoinverses in semigroups}, journal = {Proc. Cambridge Phil. Soc.}, year = {1961}, volume = {57}, pages = {247--250}, } @article {Munn99, AUTHOR = {Munn, W. D.}, TITLE = {Moore--{P}enrose inversion in complex contracted inverse semigroup algebras}, JOURNAL = JAUSMA, VOLUME = {66}, YEAR = {1999}, NUMBER = {3}, PAGES = {297--302}, MRCLASS = {20M25}, MRNUMBER = {2000e:20115}, KEYWORDS = {algsg}, } @article {MunnPenrose55, AUTHOR = {Munn, W. D. and Penrose, R.}, TITLE = {A note on inverse semigroups}, JOURNAL = PROCPS, VOLUME = {51}, YEAR = {1955}, PAGES = {396--399}, MRCLASS = {20.0X}, MRNUMBER = {17,10e}, } @article {MurakamiAibara87, AUTHOR = {Murakami, K. and Aibara, T.}, TITLE = {An improvement on the {M}oore-{P}enrose generalized inverse associative memory}, JOURNAL = {IEEE Trans. Systems Man Cybernet.}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Systems, Man, and Cybernetics}, VOLUME = {17}, YEAR = {1987}, NUMBER = {4}, PAGES = {699--707}, MRCLASS = {92A25 (92A09)}, MRNUMBER = {88g:92047}, } @article{MurnaghanWintner31, author = {F. D. Murnaghan and A. Wintner}, year = {1931}, title = {A Canonical Form for Real Matrices under Orthogonal Transformation}, journal = PRONA, volume = {17}, pages = {417-420}, KEYWORDS = {alglin, svd}, } @ARTICLE{MurrayvonNeumann36, author = {Murray, F. J. and von Neumann, J.}, title = {On rings of operators}, journal = {Ann. of Math.}, year = {1936}, volume = {37}, pages = {116--229}, } @article {MurthyRamachandran80, AUTHOR = {Murthy, K. V. V. and Ramachandran, V.}, TITLE = {On the ranks of certain matrices}, JOURNAL = {Matrix Tensor Quart.}, FJOURNAL = {The Tensor Society of Great Britain. The Matrix and Tensor Quarterly}, VOLUME = {31}, YEAR = {1980/81}, NUMBER = {3}, PAGES = {67--69}, MRCLASS = {15A15}, MRNUMBER = {82k:15008}, } @article {MurtyLakshmi90, AUTHOR = {Murty, K. N. and Lakshmi, P. V. S.}, TITLE = {On two-point boundary value problems}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {153}, YEAR = {1990}, NUMBER = {1}, PAGES = {217--225}, MRCLASS = {34B05}, MRNUMBER = {92b:34031}, } @article {MurtyRao91, AUTHOR = {Murty, M. S. N. and Rao, D. R. K. S.}, TITLE = {Application of generalized inverses to two-point boundary value problems}, JOURNAL = {Bull. Inst. Math. Acad. Sinica}, FJOURNAL = {Bulletin of the Institute of Mathematics. Academia Sinica}, VOLUME = {19}, YEAR = {1991}, NUMBER = {3}, PAGES = {271--278}, MRCLASS = {34B05 (34A09)}, MRNUMBER = {93c:34048}, } @article {MurtyAppaRao99, AUTHOR = {Murty, M. S. N. and Appa Rao, B. V.}, TITLE = {Application of {M}oore-{P}enrose inverse to three point boundary value problems}, JOURNAL = {Ranchi Univ. Math. J.}, FJOURNAL = {Ranchi University Mathematical Journal}, VOLUME = {29}, YEAR = {1998}, PAGES = {1--9 (1999)}, ISSN = {0079-9602}, MRCLASS = {34B10 (15A09 34B27)}, MRNUMBER = {2001c:34037}, } @article {NakagiriaSuzuki99, AUTHOR = {Nakagiri, S. and Suzuki, K.}, TITLE = {Finite element interval analysis of external loads identified by displacement input with uncertainty }, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {168}, YEAR = {1999}, NUMBER = {1--4}, PAGES = {63--72}, } @article {Nambooripad80, AUTHOR = {Nambooripad, K. S. Subramonian}, TITLE = {The natural partial order on a regular semigroup}, JOURNAL = {Proc. Edinburgh Math. Soc. (2)}, FJOURNAL = {Proceedings of the Edinburgh Mathematical Society. Series II}, VOLUME = {23}, YEAR = {1980}, NUMBER = {3}, PAGES = {249--260}, MRCLASS = {20M10 (06F05)}, MRNUMBER = {82g:20092}, } @ARTICLE{Nanda67, author = {Nanda, V. C.}, title = {A generalization of {C}ayley's theorem}, journal = {Math. Z.}, year = {1967}, volume = {101}, pages = {331--334}, } @book {Nash90, AUTHOR = {Nash, J. C.}, TITLE = {Compact {N}umerical {M}ethods for {C}omputers}, EDITION = {Second}, PUBLISHER = {Adam Hilger Ltd.}, ADDRESS = {Bristol}, YEAR = {1990}, PAGES = {xii+278}, ISBN = {0-85274-318-1; 0-85274-319-X}, MRCLASS = {65-04 (65F99 65K99)}, MRNUMBER = {92c:65005}, KEYWORDS = {Linear algebra, function minimisation}, } @article {NashWang86, AUTHOR = {Nash, J. C. and Wang, R. L. C.}, TITLE = {Algorithm 645: subroutines for testing programs that compute the generalized inverse of a matrix}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {12}, YEAR = {1986}, NUMBER = {3}, PAGES = {274--277}, MRCLASS = {65F20}, MRNUMBER = {889 070}, } @article {NashS84, AUTHOR = {Nash, S. G.}, TITLE = {Newton-type minimization via the {L}\'anczos method}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {21}, YEAR = {1984}, NUMBER = {4}, PAGES = {770--788}, MRCLASS = {65K10 (90C30)}, MRNUMBER = {86h:65092}, KEYWORDS = {Newton, Calculus of variations}, } @ARTICLE{Nashed70, author = {Nashed, M. Z.}, title = {Steepest descent for singular linear operator equations}, journal = SIAJN, year = {1970}, volume = {7}, pages = {358--362}, keywords = {}, } @incollection {Nashed71, AUTHOR = {Nashed, M. Z.}, TITLE = {Generalized inverses, normal solvability, and iteration for singular operator equations}, BOOKTITLE = {Nonlinear {F}unctional {A}nal. and {A}ppl. ({P}roc. {A}dvanced {S}em., {M}ath. {R}es. {C}enter, {U}niv. of {W}isconsin, {M}adison, {W}is., 1970)}, PAGES = {311--359}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1971}, MRCLASS = {47.80}, MRNUMBER = {43 \#1003}, } @proceedings{Nashed76, editor = {Nashed, M. Z.}, year = {1976}, title = {Generalized {I}nverses and {A}pplications ({P}roc. {S}em., {M}ath. {R}es. {C}enter, {U}niv. {W}isconsin, {M}adison, {W}is., 1973)}, publisher = {Academic Press}, address = {New York}, pages = {xiv + 1054 pp.}, } @inproceedings{Nashed76a, author = {Nashed, M. Z.}, title = {Generalized inverses in analysis and regularization}, crossref = {Nashed76}, year = {1976}, pages = {193--244}, } @inproceedings{Nashed76b, author = {Nashed, M. Z.}, title = {Perturbations and approximations for generalized inverses and linear operator equations}, crossref = {Nashed76}, year = {1976}, pages = {325--396}, } @article {Nashed76c, AUTHOR = {Nashed, M. Z.}, TITLE = {On moment-discretization and least-squares solutions of linear integral equations of the first kind}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {53}, YEAR = {1976}, NUMBER = {2}, PAGES = {359--366}, MRCLASS = {65R05}, MRNUMBER = {55 \#1758}, KEYWORDS = {Integral equation, least-squares solution}, } @incollection {Nashed77, AUTHOR = {Nashed, M. Z.}, TITLE = {On the perturbation theory for generalized inverse operators in {B}anach spaces}, BOOKTITLE = {Functional {A}nalysis {M}ethods in {N}umerical {A}nalysis ({P}roc. {S}pecial {S}ession, {A}nnual {M}eeting, {A}mer. {M}ath. {S}oc., {S}t. {L}ouis, {MO}, 1977)}, PAGES = {180--195}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1979}, MRCLASS = {47A55}, MRNUMBER = {80j:47018}, } @incollection {Nashed81, AUTHOR = {Nashed, M. Z.}, TITLE = {On generalized inverses and operator ranges}, BOOKTITLE = {Functional {A}nalysis and {A}pproximation ({O}berwolfach, 1980)}, PAGES = {85--96}, PUBLISHER = {Birkh\"auser}, ADDRESS = {Basel}, YEAR = {1981}, MRCLASS = {47A05}, MRNUMBER = {83i:47004}, } @article{NashedChen93, author = {Nashed, M. Z. and Chen, X.}, year = {1993}, title = {Convergence of {N}ewton-like methods for singular operator equations using outer inverses}, journal = NUMEM, volume = {66}, pages = {235--257}, } @inproceedings{NashedRall76, author = {Nashed, M. Z. and Rall, L. B.}, title = {Annotated Bibliography on Generalized Inverses and Applications}, crossref = {Nashed76}, year = {1976}, pages = {771--1041}, } @article {NashedVotruba74, AUTHOR = {Nashed, M. Z. and Votruba, G. F.}, TITLE = {A unified approach to generalized inverses of linear operators. {I}. {A}lgebraic, topological and projectional properties}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {80}, YEAR = {1974}, PAGES = {825--830}, MRCLASS = {47A50}, MRNUMBER = {51 \#1443}, } @article {NashedVotruba74a, AUTHOR = {Nashed, M. Z. and Votruba, G. F.}, TITLE = {A unified approach to generalized inverses of linear operators. {I}{I}. {E}xtremal and proximal properties}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {80}, YEAR = {1974}, PAGES = {831--835}, MRCLASS = {47A50}, MRNUMBER = {51 \#1444}, } @inproceedings{NashedVotruba76, author = {Nashed, M. Z. and Votruba, G. F.}, title = {A unified operator theory of generalized inverses}, crossref = {Nashed76}, year = {1976}, pages = {1--109}, } @article {NashedWahba74, AUTHOR = {Nashed, M. Z. and Wahba, G.}, TITLE = {Generalized inverses in reproducing kernel spaces: an approach to regularization of linear operator equations}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {5}, YEAR = {1974}, PAGES = {974--987}, MRCLASS = {47A50}, MRNUMBER = {50 \#10871}, } @article {NashedWahba74a, AUTHOR = {Nashed, M. Z. and Wahba, G.}, TITLE = {Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind}, JOURNAL = {Math. Comp.}, VOLUME = {28}, YEAR = {1974}, PAGES = {69--80}, MRCLASS = {65J05 (47A50)}, MRNUMBER = {57 \#1877}, } @incollection {NashedZhao92, AUTHOR = {Nashed, M. Z. and Zhao, Ya Gu}, TITLE = {The {D}razin inverse for singular evolution equations and partial differential operators}, BOOKTITLE = {Recent {T}rends in {D}ifferential {E}quations}, PAGES = {441--456}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1992}, MRCLASS = {47N20 (34G10 35E20 47A05 47F05)}, MRNUMBER = {93i:47114}, } @BOOK{Natterer86, author = {Natterer, F.}, title = {The {M}athematics of {C}omputerized {T}omography}, publisher = {Wiley}, year = {1986}, address = {New York}, } @ARTICLE{NelsonEtAl71, author = {Nelson, D. L. and Lewis, T. O. and Boullion, T. L.}, title = {A quadratic programming technique using matrix pseudoinverses}, journal = {Indust. Math.}, year = {1971}, volume = {21}, pages = {1--21}, } @article {Neubauer88, AUTHOR = {Neubauer, A.}, TITLE = {Tikhonov-regularization of ill-posed linear operator equations on closed convex sets}, JOURNAL = {J. Approx. Theory}, VOLUME = {53}, YEAR = {1988}, NUMBER = {3}, PAGES = {304--320}, MRCLASS = {}, MRNUMBER = {89h:65094}, } @article {Neubauer97, AUTHOR = {Neubauer, A.}, TITLE = {On converse and saturation results for {T}ikhonov regularization of linear ill-posed problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {34}, YEAR = {1997}, NUMBER = {2}, PAGES = {517--527}, MRCLASS = {65J20 (47H17)}, MRNUMBER = {98d:65081}, } @article {Neudecker69, AUTHOR = {Neudecker, H.}, TITLE = {A note on {K}ronecker matrix products and matrix equation systems}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {17}, YEAR = {1969}, PAGES = {603--606}, MRCLASS = {15.80}, MRNUMBER = {40 \#1414}, } @article {Neudecker95, AUTHOR = {Neudecker, H.}, TITLE = {Mathematical properties of the variance of the multinomial distribution}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {189}, YEAR = {1995}, NUMBER = {3}, PAGES = {757--762}, MRCLASS = {62H12}, MRNUMBER = {95k:62156}, NOTE = {(see \cite{TanabeSagae92})}, } @article {NeudeckerLiu96, AUTHOR = {Neudecker, H. and Liu, Shuangzhe}, TITLE = {The density of the {M}oore-{P}enrose inverse of a random matrix}, JOURNAL = LINAA1, VOLUME = {237/238}, YEAR = {1996}, PAGES = {123--126}, MRCLASS = {15A09 (15A52)}, MRNUMBER = {96m:15006}, } @article {Neumaier95, AUTHOR = {Neumaier, A.}, TITLE = {Hybrid norms and bounds for overdetermined linear systems}, JOURNAL = LINAA1, VOLUME = {216}, YEAR = {1995}, PAGES = {257--265}, MRCLASS = {65F20 (65F35)}, MRNUMBER = {95m:65070}, } @article {Neumaier98, AUTHOR = {Neumaier, A.}, TITLE = {Solving ill-conditioned and singular linear systems: a tutorial on regularization}, JOURNAL = SIAMR, VOLUME = {40}, YEAR = {1998}, NUMBER = {3}, PAGES = {636--666 (electronic)}, ISSN = {1095-7200}, MRCLASS = {65F30}, MRNUMBER = {99f:65066}, } @article {Neumann80, AUTHOR = {Neumann, M.}, TITLE = {On the {S}chur complement and the ${L}{U}$-factorization of a matrix}, JOURNAL = LINMA, VOLUME = {9}, YEAR = {1980/81}, NUMBER = {4}, PAGES = {241--254}, MRCLASS = {15A23}, MRNUMBER = {82g:15007}, KEYWORDS = {Schur complement}, } @article{NeumannPlemmons79, author = {M. Neumann and R. J. Plemmons}, year = {1979}, title = {Generalized Inverse-Positivity and Splittings of {M}-Matrices}, journal = LINAA1, volume = {23}, pages = {21-35}, KEYWORDS = {na, appmar, M-matrix, iter, ginv}, } @article {NeumannEtAl82, AUTHOR = {Neumann, M. and Poole, G. D. and Werner, H. {-J}.}, TITLE = {More on generalizations of matrix monotonicity}, JOURNAL = LINAA1, VOLUME = {48}, YEAR = {1982}, PAGES = {413--435}, MRCLASS = {15A09 (15A48)}, MRNUMBER = {84g:15006}, } @article {NeumannWerner91, AUTHOR = {Neumann, M. and Werner, H. {-J}.}, TITLE = {Nonnegative group inverses}, JOURNAL = LINAA1, VOLUME = {151}, YEAR = {1991}, PAGES = {85--96}, MRCLASS = {15A48 (15A09)}, MRNUMBER = {92e:15026}, } @ARTICLE{vonNeumann32, author = {von Neumann, J.}, title = {{\"U}ber adjungierte {F}unktionaloperatoren}, journal = {Ann. of Math.}, year = {1932}, volume = {33}, pages = {294--310}, } @ARTICLE{vonNeumann36, author = {von Neumann, J.}, title = {On regular rings}, journal = PRONA, year = {1936}, volume = {33}, pages = {294--310}, } @ARTICLE{vonNeumann37, author = {von Neumann, J.}, title = {Some matrix inequalities and metrization of matric--space}, journal = {Tomsk Univ. Rev.}, year = {1937}, volume = {1}, pages = {286--300}, note = {(Republished in \textit{John von Neumann Collected Works}, MacMillan, New York, Vol {IV}, pp. 205--219)}, } @BOOK{vonNeumann50, author = {von Neumann, J.}, title = {Functional {O}perators. {V}ol {II}: {T}he {G}eometry of {O}rthogonal {S}paces}, publisher = {Princeton University Press}, year = {1950}, volume = {29}, series = {Annals of Math. Studies}, address = {Princeton}, } @BOOK{vonNeumann60, author = {von Neumann, J.}, title = {Continuous {G}eometry}, publisher = {Princeton University Press}, year = {1960}, PAGES = {xi+299}, address = {Princeton}, } @INPROCEEDINGS{NewmanEtAl68, author = {Newman, T. G. and Meicler, M. and Odell, P. L.}, crossref = {BoullionOdell68}, title = {On the concept of a $p-q$ generalized inverse of a matrix}, year = {1968}, pages = {276--282}, } @ARTICLE{NewmanOdell69, author = {Newman, T. G. and Odell, P. L.}, title = {On the concept of a $p-q$ generalized inverse of a matrix}, journal = SIAJA, year = {1969}, volume = {17}, pages = {520--525}, } @article {Nievergelt94, AUTHOR = {Nievergelt, Y.}, TITLE = {Total least squares: state-of-the-art regression in numerical analysis}, JOURNAL = SIAMR, VOLUME = {36}, YEAR = {1994}, NUMBER = {2}, PAGES = {258--264}, MRCLASS = {65F20}, MRNUMBER = {95a:65077}, } @article {Nievergelt94a, AUTHOR = {Nievergelt, Y.}, TITLE = {Computing circles and spheres of arithmetic least squares}, JOURNAL = {Comput. Phys. Comm.}, VOLUME = {81}, YEAR = {1994}, NUMBER = {3}, PAGES = {343--350}, MRCLASS = {65Y25 (65U05)}, MRNUMBER = {95e:65131}, NOTE = {(extension of \cite{MouraKitney91})}, } @article {Nievergelt97, AUTHOR = {Nievergelt, Y.}, TITLE = {Schmidt-{M}irsky matrix approximation with linearly constrained singular values}, JOURNAL = LINAA1, VOLUME = {261}, YEAR = {1997}, PAGES = {207--219}, MRCLASS = {15A60 (15A18)}, MRNUMBER = {98c:15077}, } @article {Nievergelt00, AUTHOR = {Nievergelt, Y.}, TITLE = {A tutorial history of least squares with applications to astronomy and geodesy}, JOURNAL = {J. Comput. Appl. Math.}, VOLUME = {121}, YEAR = {2000}, NUMBER = {1-2}, PAGES = {37--72}, MRCLASS = {65-03 (65F20 85-08 86-08 86A30)}, MRNUMBER = {2001e:65002}, } @article {Niu01, AUTHOR = {Niu, Xing Wen}, TITLE = {Pl\"ucker coordinates representation for relations and operations between linear subspaces}, JOURNAL = {J. Math. Res. Exposition}, FJOURNAL = {Journal of Mathematical Research and Exposition}, VOLUME = {21}, YEAR = {2001}, NUMBER = {1}, PAGES = {143--147}, MRCLASS = {15A03}, MRNUMBER = {1 816 756}, } @ARTICLE{Noble66, author = {Noble, B.}, title = {A method for computing the generalized inverse of a matrix}, journal = SIAJN, year = {1966}, volume = {3}, pages = {582--584}, } @BOOK{Noble69, author = {Noble, B.}, title = {Applied {L}inear {A}lgebra}, publisher = {Prentice--Hall, Inc.}, year = {1969}, address = {Englewood Cliffs, NJ}, } @inproceedings{Noble76, author = {Noble, B.}, title = {Methods for computing the {M}oore-{P}enrose generalized inverse, and related matters}, crossref = {Nashed76}, year = {1976}, pages = {245--301}, MRCLASS = {65F20}, MRNUMBER = {57 \#11022}, } @article {Nomakuchi80, AUTHOR = {Nomakuchi, K.}, TITLE = {On characterization of generalized inverses}, JOURNAL = LINAA1, VOLUME = {33}, YEAR = {1980}, NUMBER = {}, PAGES = {1--8}, MRCLASS = {}, MRNUMBER = {}, } @article {Nordstrom89, AUTHOR = {Nordstr{\"o}m, K.}, TITLE = {Some further aspects of the {L}{\"o}wner-ordering antitonicity of the {M}oore-{P}enrose inverse}, JOURNAL = {Comm. Statist. Theory Methods}, FJOURNAL = {Communications in Statistics. Theory and Methods}, VOLUME = {18}, YEAR = {1989}, NUMBER = {12}, PAGES = {4471--4489 (1990)}, MRCLASS = {15A09 (62H12)}, MRNUMBER = {91c:15002}, } @article {Obenchain78, AUTHOR = {Obenchain, R. L.}, TITLE = {Good and optimal ridge estimators}, JOURNAL = {The Annals of Statist.}, VOLUME = {6}, YEAR = {1978}, NUMBER = {5}, PAGES = {1111--1121}, MRCLASS = {}, MRNUMBER = {}, } @article {OdellBoullion97, AUTHOR = {Odell, P. L. and Boullion, T. L.}, TITLE = {Simultaneous diagonalization of rectangular matrices}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {33}, YEAR = {1997}, NUMBER = {9}, PAGES = {93--96}, MRCLASS = {65F05 (15A21)}, MRNUMBER = {98b:65030}, } @article {OdellDecell67, AUTHOR = {Odell, P. L. and Decell, Jr., H. P.}, TITLE = {On computing the fixed-point probability vector of ergodic transition matrices}, JOURNAL = {J. Assoc. Comput. Mach.}, VOLUME = {14}, YEAR = {1967}, PAGES = {765--768}, MRCLASS = {65.25}, MRNUMBER = {38 \#2929}, } @article {Oktaba68, AUTHOR = {Oktaba, W.}, TITLE = {Tests of hypotheses for the fixed model not of full rank}, JOURNAL = {Bull. Acad. Polon. Sci. S{\'e}r. Sci. Math. Astronom. Phys.}, VOLUME = {16}, YEAR = {1968}, PAGES = {409--413}, MRCLASS = {62.55}, MRNUMBER = {38 \#828}, } @article{OLeary90, author = {O'Leary, D. P.}, year = {1990}, title = {On Bounds For Scaled Projections and Pseudo-Inverses}, journal = LINAA1, volume = {132}, pages = {115--117}, KEYWORDS = {alglin, proj, ginv}, NOTE = {(Answer to a question in \cite{Stewart89})}, } @article {Olkin98, AUTHOR = {Olkin, I.}, TITLE = {The density of the inverse and pseudo-inverse of a random matrix}, JOURNAL = {Statist. Probab. Lett.}, FJOURNAL = {Statistics \& Probability Letters}, VOLUME = {38}, YEAR = {1998}, NUMBER = {2}, PAGES = {131--135}, MRCLASS = {62H10}, MRNUMBER = {99i:62120}, NOTE = {(alternative proof to \cite{Zhang85})}, } @BOOK{OrtegaRheinboldt70, author = {Ortega, J. M. and Rheinboldt, W. C.}, title = {Iterative {S}olution of {N}onlinear {E}quations in {S}everal {V}ariables}, publisher = {Academic Press}, year = {1970}, address = {New York}, } @ARTICLE{Osborne61, author = {Osborne, E. E.}, title = {On least squares solutions of linear equations}, journal = JASSC, year = {1961}, volume = {8}, pages = {628--636}, keywords = {}, } @ARTICLE{Osborne65, author = {Osborne, E. E.}, title = {Smallest least squares solutions of linear equations}, journal = SIAJN, year = {1965}, volume = {2}, pages = {300--307}, } @article {OsborneM72, AUTHOR = {Osborne, M. R.}, TITLE = {A class of methods for minimising a sum of squares}, JOURNAL = {Austral. Comput. J.}, VOLUME = {4}, YEAR = {1972}, PAGES = {164--169}, MRCLASS = {65K05}, MRNUMBER = {47 \#7913}, } @article {Ostrowski71, AUTHOR = {Ostrowski, A.}, TITLE = {A new proof of {H}aynsworth's quotient formula for {S}chur complements. }, JOURNAL = LINAA1, VOLUME = {4}, YEAR = {1971}, PAGES = {389--392}, MRCLASS = {15.35}, MRNUMBER = {44 \#6721}, } @article {Ouellette81, AUTHOR = {Ouellette, D. V.}, TITLE = {Schur complements and statistics}, JOURNAL = LINAA1, VOLUME = {36}, YEAR = {1981}, PAGES = {187--295}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {82j:15005}, KEYWORDS = {Schur complement}, } @article {PaigeSaunders77, AUTHOR = {Paige, C. C. and Saunders, M. A.}, TITLE = {Least squares estimation of discrete linear dynamic systems using orthogonal transformations}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {14}, YEAR = {1977}, NUMBER = {2}, PAGES = {180--193}, MRCLASS = {93E10}, MRNUMBER = {55 \#10130}, } @article {PaigeSaunders81, AUTHOR = {Paige, C. C. and Saunders, M. A.}, TITLE = {Towards a generalized singular value decomposition}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {18}, YEAR = {1981}, NUMBER = {}, PAGES = {398--405}, MRCLASS = {}, MRNUMBER = {}, } @article {Pan00, AUTHOR = {Pan, C.-T.}, TITLE = {On the existence and computation of rank-revealing ${L}{U}$ factorizations}, JOURNAL = LINAA1, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {316}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {199--222}, MRCLASS = {65F05}, MRNUMBER = {1 782 425}, } @article {PanSigmon94, AUTHOR = {Pan, C.-T. and Sigmon, K.}, TITLE = {A bottom-up inductive proof of the singular value decomposition}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {15}, YEAR = {1994}, NUMBER = {1}, PAGES = {59--61}, MRCLASS = {15A18 (15A23)}, MRNUMBER = {94k:15007}, KEYWORDS = {SVD}, } @article {PanOuyang94, AUTHOR = {Pan, Ping Qi and Ouyang, Zi Xiang}, TITLE = {Moore--{P}enrose inverse simplex algorithms based on successive linear subprogramming approach}, JOURNAL = {Numer. Math. J. Chinese Univ. (English Ser.)}, VOLUME = {3}, YEAR = {1994}, NUMBER = {2}, PAGES = {180--190}, MRCLASS = {90C05 (65K05)}, MRNUMBER = {95m:90067}, KEYWORDS = {appalgo, lp, invMP}, } @article{PanSchreiber91, author = {Pan, V. and R. Schreiber, R. S.}, year = {1991}, title = {An Improved Newton Iteration for the Generalized Inverse of a Matrix with Applications}, journal = SIAJS, volume = {12}, pages = {1109--1130}, KEYWORDS = {comp, inv, ginv, Newton's method}, } @article {Pandolfi80, AUTHOR = {Pandolfi, L.}, TITLE = {Controllability and stabilization for linear systems of algebraic and differential equations}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {30}, YEAR = {1980}, NUMBER = {4}, PAGES = {601--620}, MRCLASS = {93B05 (93D15)}, MRNUMBER = {82e:93011}, } @inproceedings{Parlett67, AUTHOR = {Parlett, B. N.}, TITLE = {The \textit{LU} and \textit{QR} algorithms}, CROSSREF = {RalstonWilf67}, PAGES = {116--130, Vol. {II}}, YEAR = {1967}, } @article {Parshall84, AUTHOR = {Parshall, K. H.}, TITLE = {{E}liakim {H}astings {M}oore and the founding of a mathematical community in {A}merica}, JOURNAL = {Annals of Science}, VOLUME = {41}, YEAR = {1984}, PAGES = {313--333}, MRCLASS = {}, MRNUMBER = {}, KEYWORDS = {History, Moore}, NOTE = {(reprinted in \textit{A {C}entury of {M}ethematics in {A}merica -- {P}art {II}}, ed. Peter Duren et al, American Mathematical Society, 1989, pp. 155--175)}, } @book {ParshallRowe94, AUTHOR = {Parshall, K. H. and Rowe, D. E.}, TITLE = {The {E}mergence of the {A}merican {M}athematical {R}esearch {C}ommunity, 1876--1900: {J}. {J}. {S}ylvester, {F}elix {K}lein, and {E}. {H}. {M}oore}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {1994}, PAGES = {xxiv+500}, ISBN = {0-8218-9004-2}, MRCLASS = {01A72 (01A55)}, MRNUMBER = {95j:01032}, } @article {Pati00, AUTHOR = {Pati, S.}, TITLE = {Moore--{P}enrose inverse of matrices on idempotent semirings}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, VOLUME = {22}, YEAR = {2000}, NUMBER = {2}, PAGES = {617--626 (electronic)}, MRCLASS = {15A09}, MRNUMBER = {1 781 507}, } @inproceedings{Pavel-ParvuKorganoff69, author = {Pavel-Parvu, M. and Korganoff, A.}, year = {1969}, title = {Iteration Functions for Solving Polynomial Equations}, booktitle = {Constructive {A}spects of the {F}undamental {T}heorem of {A}lgebra}, editor = {B. Dejon and P. Henrici}, pages = {}, publisher = {John Wiley}, address = {New York}, KEYWORDS = {alglin, ginv, matder}, } @article{Peano1888, author = {G. Peano}, year = {1888}, title = {Int\'egration par s\'eries des \'equations diff\'erentielles lin\'eaires}, journal = {Mathematische Annallen}, volume = {32}, pages = {450-456}, KEYWORDS = {svd, diff}, } @article {Pearl57, AUTHOR = {Pearl, M. H.}, TITLE = {On {C}ayley's parametrization}, JOURNAL = {Canad. J. Math.}, VOLUME = {9}, YEAR = {1957}, PAGES = {553--562}, } @article {Pearl59a, AUTHOR = {Pearl, M. H.}, TITLE = {A further extension of {C}ayley's parametrization}, JOURNAL = {Canad. J. Math.}, VOLUME = {11}, YEAR = {1959}, PAGES = {48--50}, } @article {Pearl59, AUTHOR = {Pearl, M. H.}, TITLE = {On normal and ${E}{P}\sb{r}$ matrices}, JOURNAL = {Michigan Math. J.}, VOLUME = {6}, YEAR = {1959}, PAGES = {1--5}, MRCLASS = {15.00}, MRNUMBER = {21 \#1976}, KEYWORDS = {matEP}, } @article {Pearl61, AUTHOR = {Pearl, M. H.}, TITLE = {On normal ${EP}\sb{r}$ matrices}, JOURNAL = {Michigan Math. J.}, VOLUME = {8}, YEAR = {1961}, PAGES = {33--37}, MRCLASS = {15.30}, MRNUMBER = {23 \#A161}, KEYWORDS = {matEP}, } @article {Pearl66, AUTHOR = {Pearl, M. H.}, TITLE = {On generalized inverses of matrices}, JOURNAL = {Proc. Cambridge Philos. Soc.}, VOLUME = {62}, YEAR = {1966}, PAGES = {673--677}, MRCLASS = {15.15}, MRNUMBER = {33 \#5650}, KEYWORDS = {matEP, invMP}, } @article {Pearl67, AUTHOR = {Pearl, M. H.}, TITLE = {A decomposition theorem for matrices}, JOURNAL = {Canad. J. Math.}, VOLUME = {19}, YEAR = {1967}, PAGES = {344--349}, MRCLASS = {15.30}, MRNUMBER = {35 \#1610}, KEYWORDS = {svd}, NOTE = {(see \cite{Thompson69}, \cite{Wiegmann48})}, } @article{Pearl68, AUTHOR = {Pearl, M. H.}, TITLE = {Generalized inverses of matrices with entries taken from an arbitrary field}, JOURNAL = LINAA1, VOLUME = {1}, YEAR = {1968}, PAGES = {571--587}, MRCLASS = {15.15}, KEYWORDS = {algf}, MRNUMBER = {40 \#158}, NOTE = {(see also \cite{Rieck00})}, } @article {Pearl84, AUTHOR = {Pearl, M. H.}, TITLE = {Automorphic transformations of an arbitrary matrix}, JOURNAL = {Linear and Multilinear Algebra}, VOLUME = {15}, YEAR = {1984}, NUMBER = {3-4}, PAGES = {245--256}, MRCLASS = {15A21}, MRNUMBER = {85e:15018}, KEYWORDS = {Cayley transform}, } @article{Pearson1901, author = {K. Pearson}, year = {1901}, title = {On Lines and Planes of Closest Fit to Points in Space}, journal = {Philosophical Magazine}, volume = {2}, pages = {559--572}, KEYWORDS = {appst, svd, lsqtot}, } @article {PelusoPiazza99, AUTHOR = {Peluso, R. and Piazza, G.}, TITLE = {Bounds for products of singular values of a matrix}, JOURNAL = {Rend. Mat. Appl. (7)}, FJOURNAL = {Rendiconti di Matematica e delle sue Applicazioni. Serie VII}, VOLUME = {19}, YEAR = {1999}, NUMBER = {4}, PAGES = {507--522 (2000)}, MRCLASS = {15A42}, MRNUMBER = {1 789 485}, } @BOOK{Pennington70, author = {Pennington, R. H.}, title = {Introductory {C}omputer {M}ethods and {N}umerical {A}nalysis}, publisher = {MacMillan Co.}, year = {1970}, address = {New York}, } @article{Penrose55, author = {Penrose, R.}, year = {1955}, title = {A Generalized Inverse for Matrices}, journal = PROCPS, volume = {51}, pages = {406--413}, KEYWORDS = {alglin, invMP, svd, his}, } @article{Penrose56, author = {Penrose, R.}, year = {1956}, title = {On Best Approximate Solutions of Linear Matrix Equations}, journal = PROCPS, volume = {52}, pages = {17-19}, KEYWORDS = {alglin, invMP, sollsq, solmin}, } @article{Pereyra67, author = {Pereyra, V.}, year = {1967}, title = {Iterative Methods for Solving Nonlinear Least Squares Problems}, journal = SIAJN, volume = {4}, pages = {27--36}, KEYWORDS = {compit, lsqnl}, } @article{Pereyra69, author = {Pereyra, V.}, year = {1969}, title = {Stability of General Systems of Linear Equations}, journal = {Aequationes Mathematicae}, volume = {2}, pages = {194--206}, KEYWORDS = {alglin, pert, ginv}, } @TECHREPORT{PereyraRosen64, author = {Pereyra, V. and Rosen, J. B.}, title = {Computation of the pseudoinverse of a matrix of unknown rank}, institution = {Dept. of Computer Science, Stanford University}, year = {1964}, month = {Sept.}, number = {CS 13}, address = {Stanford, CA}, keywords = {}, note = {(\textit{Comp. Rev.}\textbf{6}(1965), 259 \#7948)}, } @article{PetersWilkinson70, author = {Peters, G. and Wilkinson, J. H.}, year = {1970}, title = {The Least Squares Problem and Pseudo-Inverses}, journal = COMPJ, volume = {13}, pages = {309--316}, KEYWORDS = {comp, lsq, ginv}, } @ARTICLE{Petryshyn67, author = {Petryshyn, W. V.}, title = {On generalized inverses and on the uniform convergence of $({I}-\beta {K})^n$ with application to iterative methods}, journal = JMATA, year = {1967}, volume = {18}, pages = {417--439}, keywords = {}, } @article {Phillips62, AUTHOR = {Phillips, D. L.}, TITLE = {A technique for the numerical solution of certain integral equations of the first kind}, JOURNAL = {J. Assoc. Comput. Mach.}, VOLUME = {9}, YEAR = {1962}, PAGES = {84--97}, MRCLASS = {65.75}, MRNUMBER = {24 \#B534}, MRREVIEWER = {E. J. Scott}, } @article {Picon99, AUTHOR = {Pic{\'o}n, R.}, TITLE = {A systematic deduction of linear natural approach equations}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {177}, YEAR = {1999}, PAGES = {137--151}, KWDS = {Finite Elements}, } @article {Pierce96, AUTHOR = {Pierce, W. H.}, TITLE = {A self-correcting matrix iteration for the {M}oore-{P}enrose generalized inverse}, JOURNAL = LINAA1, VOLUME = {244}, YEAR = {1996}, PAGES = {357--363}, MRCLASS = {15A09}, MRNUMBER = {97d:15008}, } @article{Pietsch60, AUTHOR = {Pietsch, A.}, TITLE = {Zur {T}heorie der $\sigma$--{T}ransformationen in lokalkonvexen {V}ektorr{\"a}umen}, JOURNAL = {Math. Nach.}, VOLUME = {21}, YEAR = {1960}, PAGES = {347--369}, } @article {PiziakEtAl99, AUTHOR = {Piziak, R. and Odell, P. L. and Hahn, R.}, TITLE = {Constructing projections on sums and intersections}, JOURNAL = {Comput. Math. Appl.}, VOLUME = {37}, YEAR = {1999}, NUMBER = {1}, PAGES = {67--74}, MRCLASS = {65F25}, MRNUMBER = {99i:65047}, } @article {Plackett50, AUTHOR = {Plackett, R. L.}, TITLE = {Some theorems in least squares}, JOURNAL = {Biometrika}, VOLUME = {37}, YEAR = {1950}, PAGES = {149--157}, MRCLASS = {62.0X}, MRNUMBER = {12,194d}, } @article {Plemmons71, AUTHOR = {Plemmons, R. J.}, TITLE = {Generalized inverses of {B}oolean relation matrices}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {20}, YEAR = {1971}, PAGES = {426--433}, MRCLASS = {15.15}, MRNUMBER = {44 \#4015}, } @article {PlemmonsCline72, AUTHOR = {Plemmons, R. J. and Cline, R. E.}, TITLE = {The generalized inverse of a nonnegative matrix}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {31}, YEAR = {1972}, PAGES = {46--50}, MRCLASS = {15.15}, MRNUMBER = {44 \#2759}, NOTE = {(erratum, \textit{ibid} \textbf{39}(1972), 651)}, } @article {PoggioGirosi90, AUTHOR = {Poggio, T. and Girosi, F.}, TITLE = {Regularization algorithms for learning that are equivalent to multilayer networks}, JOURNAL = {Science}, FJOURNAL = {American Association for the Advancement of Science. Science}, VOLUME = {247}, YEAR = {1990}, NUMBER = {4945}, PAGES = {978--982}, MRCLASS = {92A25 (41A15 68T05 92A09)}, MRNUMBER = {90k:92076}, KEYWORDS = {Generalized splines, regularization, approximation}, } @incollection {Pokorna80, AUTHOR = {Pokorn{\'a}, Olga}, TITLE = {On the pseudoinversion of matrix products}, BOOKTITLE = {Numerical {M}ethods ({T}hird {C}olloq., {K}eszthely, 1977)}, PAGES = {501--506}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1980}, MRCLASS = {65F20}, MRNUMBER = {81m:65058}, KEYWORDS = {Reverse law}, } @Article{PolzleitnerWechsler90, author = {P{\"o}lzleitner, W. and Wechsler, H.}, title = {Selective and Focused Invariant Recognition Using Distributed Associative Memories ({DAM})}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {12}, number = {8}, pages = {809--814}, year = {1990}, } @article {PooleBarker79, AUTHOR = {Poole, G. D. and Barker, G. P.}, TITLE = {M{P} matrices}, JOURNAL = LINAA1, VOLUME = {26}, YEAR = {1979}, PAGES = {165--174}, MRCLASS = {15A09}, MRNUMBER = {80e:15004}, } @article {PooleBoullion72, AUTHOR = {Poole, G. D. and Boullion, T. L.}, TITLE = {Weak spectral inverses which are partial isometries}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {23}, YEAR = {1972}, PAGES = {171--172}, MRCLASS = {15A09}, MRNUMBER = {47 \#5011}, } @article {PooleBoullion72a, AUTHOR = {Poole, G. D. and Boullion, T. L.}, TITLE = {The {D}razin inverse for certain power matrices}, JOURNAL = {Indust. Math.}, VOLUME = {22}, YEAR = {1972}, PAGES = {35--37}, MRCLASS = {15A09}, MRNUMBER = {46 \#9059}, } @article {PooleBoullion75, AUTHOR = {Poole, G. D. and Boullion, T. L.}, TITLE = {The {D}razin inverse and a spectral inequality of {M}arcus, {M}inc, and {M}oyls}, JOURNAL = {J. Optimization Theory Appl.}, VOLUME = {15}, YEAR = {1975}, PAGES = {503--508}, MRCLASS = {15A42}, MRNUMBER = {51 \#3196}, } @BOOK{Porter66, author = {Porter, W. A.}, title = {Modern {F}oundations of {S}ystem {E}ngineering}, publisher = {MacMillan}, year = {1966}, pages = {xii+493 pp.}, address = {New York}, } @ARTICLE{Porter71, author = {Porter, W. A.}, title = {A basic optimization problem in linear systems}, journal = {Math. Syst. Th.}, year = {1971}, volume = {5}, pages = {20--44}, } @ARTICLE{PorterWilliams66, author = {Porter, W. A. and Williams, J. P.}, title = {A note on the minimum effort control problem}, journal = JMATA, year = {1966}, volume = {13}, pages = {251--264}, } @ARTICLE{PorterWilliams66a, author = {Porter, W. A. and Williams, J. P.}, title = {Extension of the minimum effort control problem}, journal = JMATA, year = {1966}, volume = {13}, pages = {536--549}, } @inproceedings{Prasad94, AUTHOR = {Prasad, K. M.}, TITLE = {Generalized inverses of matrices over commutative rings}, CROSSREF = {BapatEtAl94}, YEAR = {1994}, PAGES = {35--52}, MRCLASS = {15A09 (15A33)}, KEYWORDS = {algr, invMP, detCr}, MRNUMBER = {95m:15007}, } @article {PrasadBapat92, AUTHOR = {Prasad, K. M. and Bapat, R. B.}, TITLE = {A note on the {K}hatri--inverse}, JOURNAL = {Sankhy\=a Ser. A}, FJOURNAL = {Sankhy\=a. The Indian Journal of Statistics. Series A}, VOLUME = {54}, YEAR = {1992}, NUMBER = {2}, PAGES = {291--295}, MRCLASS = {15A09}, MRNUMBER = {93m:15007}, } @article {PrasadBapat92a, AUTHOR = {Prasad, K. M. and Bapat, R. B.}, TITLE = {The generalized {M}oore-{P}enrose inverse}, JOURNAL = LINAA1, VOLUME = {165}, YEAR = {1992}, PAGES = {59--69}, MRCLASS = {15A09}, MRNUMBER = {93a:15005}, } @article {PrasadEtAl91, AUTHOR = {Prasad, K. M. and Rao, K. P. S. Bhaskara and Bapat, R. B.}, TITLE = {Generalized inverses over integral domains. {I}{I}. {G}roup inverses and {D}razin inverses}, JOURNAL = LINAA1, VOLUME = {146}, YEAR = {1991}, PAGES = {31--47}, MRCLASS = {15A09 (15A33)}, MRNUMBER = {92a:15006}, } @article {PrattDavarian77, AUTHOR = {Pratt, William K. and Davarian, Faramarz}, TITLE = {Fast computational techniques for pseudoinverse and {W}iener image restoration}, JOURNAL = {IEEE Trans. Computers}, VOLUME = {C-26}, YEAR = {1977}, NUMBER = {6}, PAGES = {571--580}, MRCLASS = {94A05}, MRNUMBER = {58 \#15655}, } @article {Preston54, AUTHOR = {Preston, G. B.}, TITLE = {Inverse semi-groups}, JOURNA