GI.bib
@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 = {Computing},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Appl. Math.},
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 = {SIAM J. Appl. Math.},
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 = {Amer. Math. Monthly},
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 = {SIAM J. Appl. Math.},
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 = {SIAM J. Appl. Math.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Trans. Amer. Math. Soc.},
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 = {Numer. Math.},
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 = {Linear Algebra and its Applications},
VOLUME = {82},
YEAR = {1986},
PAGES = {163--167}
}
@ARTICLE{Baksalary02,
AUTHOR = {Baksalary, J. K. and Baksalary, O. M.},
TITLE = {Commutativity of projectors},
JOURNAL = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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{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 = {Linear Algebra and its Applications},
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 = {Proc. Roy. Soc. London Ser. A},
VOLUME = {100},
PAGES = {441--449},
KEYWORDS = {comp, svd, inteq}
}
@ARTICLE{Batigne78,
AUTHOR = {Batigne, D.},
TITLE = {Integral generalized inverses of integral matrices},
JOURNAL = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Numer. Math.},
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 = {J. Math. Anal. Appl.},
YEAR = {1969},
VOLUME = {26},
PAGES = {297--306}
}
@ARTICLE{Ben-Israel64,
AUTHOR = {Ben-Israel, A.},
TITLE = {On direct sum decompositions of {H}estenes algebras},
JOURNAL = {Israel J. Math.},
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 = {Math. Comput.},
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 = {Israel J. Math.},
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 = {SIAM J. Numer. Anal.},
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 = {J. Math. Anal. Appl.},
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 = {Math. Comput.},
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 = {SIAM J. Appl. Math.},
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 = {Israel J. Math.},
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 = {SIAM J. Appl. Math.},
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 = {SIAM Rev.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Matrix Anal. Appl.},
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 = {Linear Algebra and its Applications},
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 = {J. Math. Anal. Appl.},
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 = {Operations Res.},
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 = {SIAM J. Numer. Anal.},
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 = {J. Assoc. Comput. Mach.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Sci. Comput.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {J. Math. Anal. Appl.},
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 = {J. Math. Anal. Appl.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Bull. Amer. Math. Soc.},
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 = {Bull. Amer. Math. Soc.},
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 = {Bull. Amer. Math. Soc.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {IEEE Trans. Automatic Control},
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 = {Trans. Amer. Math. Soc.},
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 = {Numer. Math.},
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 = {SIAM J. Appl. Math.},
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 = {Pacific J. Math.},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Proc. Roy. Soc. London Ser. A},
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 = {SIAM J. Appl. Math.},
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 = {Numer. Math.},
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 = {Comm. ACM},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Appl. Math.},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Appl. Math.},
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 = {Linear and Multilinear Algebra},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {SIAM J. Appl. Math.},
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 = {Linear Algebra and its Applications},
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 = {Operations Res.},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear Algebra and its Applications},
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 = {Linear and Multilinear Algebra},
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 = {Linear and Multilinear Algebra},
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 = {Linear and Multilinear Algebra},
VOLUME = {40},
YEAR = {1995},
NUMBER = {1},
PAGES = {61--68},