%% 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. 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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. 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Math. 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Proc. Cambridge Philos. 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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. 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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. 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