GI.bib
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\lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} }}
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@PREAMBLE{{\def\cprime{$'$} }}
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AUTHOR = {Arghiriade, E.},
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YEAR = {1980},
NUMBER = {5-6},
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MRNUMBER = {86a:15030}
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}
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ISSN = {0319-5724},
MRCLASS = {62J05},
MRNUMBER = {86f:62100a},
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}
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YEAR = {1990},
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}
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YEAR = {1991},
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}
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MRCLASS = {15A99},
MRNUMBER = {92e:15036}
}
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}
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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},
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YEAR = {1998},
PAGES = {31--39},
MRCLASS = {15A09 (15A48)},
MRNUMBER = {98m:15009},
KEYWORDS = {matmon}
}
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JOURNAL = {Linear Algebra and its Applications},
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YEAR = {1999},
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MRNUMBER = {2000h:15006}
}
@ARTICLE{Bapat99a,
AUTHOR = {Bapat, R. B.},
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JOURNAL = {Mathematics Student},
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YEAR = {1999},
PAGES = {87--98}
}
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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}
}
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AUTHOR = {Bapat, R. B. and Rao, K. P. S. Bhaskara and Prasad, K. M.},
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VOLUME = {140},
YEAR = {1990},
PAGES = {181--196},
MRCLASS = {15A09},
KEYWORDS = {algid, discr},
MRNUMBER = {91i:15006}
}
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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}
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Equations Occurring in the Theory of Integral
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KEYWORDS = {comp, svd, inteq}
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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}
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AUTHOR = {Berman, A. and Plemmons, R. J.},
TITLE = {Nonnegative {M}atrices in the {M}athematical {S}ciences},
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YEAR = {1994},
PAGES = {xx+340},
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AUTHOR = {Berryman, Kenneth W. and Inchiosa, Mario E. and Jaffe, Arthur
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TITLE = {Extending the pseudoinverse rule},
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PAGES = {169--175},
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YEAR = {1990},
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MRNUMBER = {92f:92048}
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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},
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Practice of Inverse Problems, Inverse Methods and Computerized
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VOLUME = {1},
YEAR = {1985},
NUMBER = {4},
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MRCLASS = {45E99 (41A15 65J10)},
MRNUMBER = {87e:45005}
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AUTHOR = {Bertero, M. and De Mol, C. and Pike, E. R.},
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JOURNAL = {Inverse Problems},
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Inversion of Data},
VOLUME = {4},
YEAR = {1988},
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MRNUMBER = {90a:65127}
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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}
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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}
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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}
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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}
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AUTHOR = {Bevis, J. H. and Hall, F. J. and Katz, I. J.},
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VOLUME = {39},
YEAR = {1981},
PAGES = {247--258},
MRCLASS = {15A09 (05C50)},
MRNUMBER = {82k:15004}
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AUTHOR = {Bevis, J. H. and Hall, F. J. and Hartwig, R. E.},
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JOURNAL = {Linear Algebra and its Applications},
VOLUME = {97},
YEAR = {1987},
PAGES = {229--242},
MRCLASS = {15A09 (15A21)},
KEYWORDS = {invD},
MRNUMBER = {88i:15006}
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AUTHOR = {Bevis, J. H. and Hall, F. J. and Hartwig, R. E.},
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PAGES = {51--64},
PUBLISHER = {North-Holland},
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MRCLASS = {15A24 (15A21)},
MRNUMBER = {89a:15015}
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@BOOK{Bhatia87,
AUTHOR = {Bhatia, R.},
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YEAR = {1987},
PAGES = {viii+129},
ISBN = {0-582-01379-8},
MRCLASS = {15A42 (15A60 47A55 65F15)},
MRNUMBER = {88k:15020}
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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}.
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NUMBER = {1-2},
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AUTHOR = {Bhimasankaram, P.},
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VOLUME = {36},
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NUMBER = {2},
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MRCLASS = {15A09 (62J05)},
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VOLUME = {109},
YEAR = {1988},
PAGES = {131--143},
MRCLASS = {15A09},
MRNUMBER = {89j:15007}
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AUTHOR = {Bhimasankaram, P.},
TITLE = {Rank factorization of a matrix and its applications},
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YEAR = {1988},
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PAGES = {4--14},
MRCLASS = {15A23},
MRNUMBER = {90b:15009a},
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@ARTICLE{BhimasankaramMathew93,
AUTHOR = {Bhimasankaram, P. and Mathew, T.},
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VOLUME = {183},
YEAR = {1993},
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MRCLASS = {15A09},
MRNUMBER = {93m:15005}
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@ARTICLE{BhimasankaramSahaRay97,
AUTHOR = {Bhimasankaram, P. and SahaRay, R.},
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YEAR = {1986},
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AUTHOR = {Birkhoff, G. D.},
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@BOOK{Birnbaum62,
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YEAR = {1962},
PAGES = {viii+325},
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JOURNAL = {Bull. G\'eod\'esique},
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AUTHOR = {Bjerhammar, A.},
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VOLUME = {85},
YEAR = {1967},
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MRCLASS = {15.15},
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@BOOK{Bjerhammar73,
AUTHOR = {Bjerhammar, A.},
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PAGES = {xii+420},
MRCLASS = {62-02 (15A09 65FXX 93E10)},
MRNUMBER = {49 \#1626}
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AUTHOR = {Bj{\"o}rck, {\AA}.},
TITLE = {Solving linear least squares problems by {G}ram--{S}chmidt orthogonalization},
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VOLUME = {7},
YEAR = {1967},
PAGES = {1--21}
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AUTHOR = {Bj{\"o}rck, {\AA}.},
TITLE = {Iterative refinement of linear least squares solutions {I}},
JOURNAL = {BIT},
VOLUME = {7},
YEAR = {1967},
PAGES = {257--278}
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@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}
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@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}
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@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 = {}
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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 = {}
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@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}
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@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}
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@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}
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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},
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AUTHOR = {Blattner, J. W.},
TITLE = {Bordered matrices},
JOURNAL = {J. Soc. Indust. Appl. Math.},
VOLUME = {10},
YEAR = {1962},
PAGES = {528--536},
MRCLASS = {65.40},
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MRNUMBER = {27 \#2098}
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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},
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PAGES = {43--46},
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MRNUMBER = {32 \#1885}
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JOURNAL = {Bull. Amer. Math. Soc.},
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YEAR = {1934},
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KEYWORDS = {History, Moore}
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@PREAMBLE{{\def\polhk#1{\setbox0=\hbox{#1}{\ooalign{\hidewidth
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AUTHOR = {Bober, L. and Chrzan, P.},
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Przegl\polhk ad Statystyczny},
VOLUME = {25},
YEAR = {1978},
NUMBER = {3},
PAGES = {315--324 (1979)},
MRCLASS = {62J05},
MRNUMBER = {81b:62080}
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VOLUME = {307},
YEAR = {2000},
NUMBER = {1-3},
PAGES = {69--75},
ISSN = {0024-3795},
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AUTHOR = {Boggs, P. T.},
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JOURNAL = {Math. Comp.},
VOLUME = {30},
YEAR = {1976},
NUMBER = {135},
PAGES = {512--522},
MRCLASS = {65K05 (34D20)},
MRNUMBER = {54 \#4095}
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AUTHOR = {Bohl, E. and Lancaster, P.},
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JOURNAL = {Linear Algebra and its Applications},
VOLUME = {180},
YEAR = {1993},
PAGES = {35--59},
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MRNUMBER = {94a:34075}
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AUTHOR = {Boman, E. and Koltracht, I.},
TITLE = {Computing preconditioners via subspace projection},
JOURNAL = {Linear Algebra and its Applications},
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VOLUME = {302/303},
YEAR = {1999},
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MRNUMBER = {2000i:65040}
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AUTHOR = {Bohnenblust, F.},
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PAGES = {103--109}
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@BOOK{BonnesenFenchel34,
AUTHOR = {Bonnesen, T. and Fenchel, W.},
TITLE = {Theorie der konvexen {K}{\"o}rper},
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ADDRESS = {Berlin}
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AUTHOR = {Boor, C. de},
TITLE = {The {M}ethod of {P}rojections as applied to the
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SCHOOL = {University of Michigan},
YEAR = {1966},
TYPE = {Doctoral dissertation in Mathematics},
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@ARTICLE{deBoor81,
AUTHOR = {Boor, C. de},
TITLE = {Convergence of abstract splines},
JOURNAL = {J. Approx. Theory},
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VOLUME = {31},
YEAR = {1981},
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MRCLASS = {41A65 (41A15 41A50)},
MRNUMBER = {82h:41042}
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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},
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AUTHOR = {Boro{\c{s}}, E.},
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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}
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@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}
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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}
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AUTHOR = {Boro{\c{s}}, E.},
TITLE = {The generalized inverse of linear operators on spaces with
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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
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VOLUME = {21},
YEAR = {1983},
NUMBER = {1-2},
PAGES = {9--44},
MRCLASS = {47B50 (47A05)},
MRNUMBER = {85h:47042}
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@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}
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@ARTICLE{BoseMitra78,
AUTHOR = {Bose, N. K. and Mitra, S. K.},
TITLE = {Generalized inverse of polynomial matrices},
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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},
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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 ${A}\sp {T}{X}\pm {X}\sp {T}{A}={B}$},
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VOLUME = {20},
YEAR = {1999},
NUMBER = {2},
PAGES = {295--302 (electronic)},
MRCLASS = {15A24 (15A09 58F07 70H05)},
MRNUMBER = {99h:15014}
}
@ARTICLE{Bradley66,
AUTHOR = {Bradley, J. S.},
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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}
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@ARTICLE{Brand62,
AUTHOR = {Brand, L.},
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JOURNAL = {Math. Gaz.},
YEAR = {1962},
VOLUME = {46},
PAGES = {203--237},
KEYWORDS = {}
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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.},
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VOLUME = {15},
YEAR = {1994},
NUMBER = {3},
PAGES = {922--937},
MRCLASS = {65F30 (65B99)},
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@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}
}
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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}
}
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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}
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@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}
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@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}
}
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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)}
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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}
}
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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 = {},
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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}
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AUTHOR = {Catlin, D. E.},
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ADDRESS = {New York},
YEAR = {1989},
PAGES = {xiii+274},
MRCLASS = {},
MRNUMBER = {},
NOTE = {(see, in particular, pp. 100--113)},
KEYWORDS = {Kalman filter, estimation}
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AUTHOR = {Cen, Jian Miao},
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NUMBER = {3},
PAGES = {453--458}
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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},
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YEAR = {2000},
MRCLASS = {41A65 (41A35 46B20 46E30)},
MRNUMBER = {1 782 730}
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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}
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AUTHOR = {Charnes, A. and Cooper, W. W.},
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JOURNAL = {Naval Res. Logist. Quart.},
YEAR = {1968},
VOLUME = {15},
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KEYWORDS = {}
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@ARTICLE{CharnesEtAl65,
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JOURNAL = {Management Sci.},
YEAR = {1965},
VOLUME = {12},
PAGES = {83--112}
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@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}
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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}
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@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},
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YEAR = {1998},
NUMBER = {4},
PAGES = {405--410},
MRCLASS = {49K40 (47A05)},
MRNUMBER = {1 667 326},
NOTE = {(translation in
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@ARTICLE{ChenG-XueY97,
AUTHOR = {Chen, Guoliang and Xue, Yifeng},
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NUMBER = {1},
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MRCLASS = {47A50 (47A05)},
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@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},
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YEAR = {1998},
NUMBER = {1-3},
PAGES = {1--6},
MRCLASS = {47A05 (47A55 65J10)},
MRNUMBER = {99k:47002}
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@ARTICLE{Chen82,
AUTHOR = {Chen, Han Fu},
TITLE = {Two kinds of linear estimators in {H}ilbert spaces, and their connection},
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VOLUME = {25},
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NUMBER = {1-3},
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MRNUMBER = {1 810 097}
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AUTHOR = {Dokovi{\'c}, Dragomir {\v{Z}}.},
TITLE = {On the generalized inverse for matrices},
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Hrvatske},
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YEAR = {1965},
PAGES = {51--55},
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PAGES = {33--36},
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YEAR = {1987},
MRCLASS = {15A09},
MRNUMBER = {90a:15002}
}
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YEAR = {1969},
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}
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YEAR = {1963},
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MRCLASS = {15.15},
MRNUMBER = {30 \#2024}
}
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AUTHOR = {Dragomir, P.},
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JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.},
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YEAR = {1964},
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}
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MRNUMBER = {58 \#6003}
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CROSSREF = {Campbell82a},
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YEAR = {1982},
MRCLASS = {15A09},
MRNUMBER = {83k:15005},
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}
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JOURNAL = {J. Algebra},
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YEAR = {1986},
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VOLUME = {165},
YEAR = {1992},
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MRNUMBER = {2000f:62174}
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AUTHOR = {Drygalla, V.},
TITLE = {Zur {D}arstellung und {B}erechnung von verallgemeinerten inversen {M}atrizen},
SCHOOL = {Martin-Luther Universit{\"a}t},
YEAR = {1980},
TYPE = {Mathematics Dissertation},
ADDRESS = {Halle-Wirtenberg}
}
@PREAMBLE{{\def\cprime{$'$} }}
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AUTHOR = {Drygalla, V.},
TITLE = {Refinement of pseudosolutions of a system of linear equations},
JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.},
FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u \i \
Matematiki i Matematichesko\u \i \ Fiziki},
VOLUME = {22},
YEAR = {1982},
NUMBER = {5},
PAGES = {1027--1032, 1275},
MRCLASS = {65F10 (15A09)},
MRNUMBER = {84a:65026},
NOTE = {(English translation: \textit{U.S.S.R. Comput. Math. and Math. Phys} \textbf{22}(1982), 1--7)}
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AUTHOR = {Drygalla, V.},
TITLE = {Zur {B}erechnung von {L}\"osungen konsistenter linearer
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VOLUME = {36},
YEAR = {1986},
NUMBER = {1-2},
PAGES = {163--168},
MRCLASS = {65F05 (65F10)},
MRNUMBER = {87d:65031}
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JOURNAL = {Unternehmensforschung},
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YEAR = {1969},
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MRCLASS = {90.58},
MRNUMBER = {44 \#3701}
}
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YEAR = {1970},
PAGES = {viii+113},
MRCLASS = {62.55},
MRNUMBER = {43 \#7016}
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YEAR = {1975},
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MRCLASS = {62J05},
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}
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VOLUME = {24},
YEAR = {1976},
NUMBER = {12},
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MRCLASS = {62J05},
MRNUMBER = {55 \#9425}
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AUTHOR = {Duffin, R. J.},
CROSSREF = {WilfHarary71},
TITLE = {Network models},
YEAR = {1971},
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AUTHOR = {Duffin, R. J. and Morley, T. D.},
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YEAR = {1979},
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MRCLASS = {94C05},
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}
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AUTHOR = {Duffin, R. J. and Morley, T. D.},
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PAGES = {27--49},
YEAR = {1982},
MRCLASS = {94C05},
KEYWORDS = {appnet, parsum},
MRNUMBER = {84h:94020a}
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JOURNAL = {Applicable Anal.},
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YEAR = {1972/73},
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YEAR = {1971},
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AUTHOR = {Egerv{\'a}ry, E.},
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NUMBER = {3},
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MRNUMBER = {89h:65049}
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AUTHOR = {Eisenstat, S. C. and Ipsen, I. C. F.},
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VOLUME = {27},
YEAR = {1978},
NUMBER = {4},
PAGES = {651--652},
MRCLASS = {93B15},
MRNUMBER = {57 \#9179},
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AUTHOR = {Eld\'en. L.},
YEAR = {1983},
TITLE = {A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems},
JOURNAL = {BIT},
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YEAR = {1998},
NUMBER = {2},
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MRCLASS = {65F10 (65F50)},
MRNUMBER = {99d:65105}
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AUTHOR = {El Ghaoui, L. and Lebret, H.},
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AUTHOR = {Elliott, W. W.},
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AUTHOR = {Elliott, W. W.},
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YEAR = {1929},
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YEAR = {1998},
NUMBER = {1-3},
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YEAR = {1969},
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YEAR = {1966},
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@PREAMBLE{{\def\cprime{$'$} }}
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PAGES = {55--60},
PUBLISHER = {Gauthiers--Villars},
ADDRESS = {Paris},
YEAR = {1962},
MRNUMBER = {29 \#2953}
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ADDRESS = {Berlin},
YEAR = {1978},
MRCLASS = {65K05 (90C30)},
MRNUMBER = {58 \#13708},
KEYWORDS = {Nonlinear equations}
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YEAR = {1978},
NUMBER = {1},
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YEAR = {1979},
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MRNUMBER = {80i:15004}
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VOLUME = {76},
YEAR = {1986},
PAGES = {1--17},
MRCLASS = {60J10 (65F35)},
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JOURNAL = {Stud. Cerc. Mat.},
YEAR = {1965},
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PAGES = {107--122},
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PAGES = {83--93}
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YEAR = {1975},
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VOLUME = {20},
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YEAR = {1965},
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JOURNAL = {K\"ozlem\'enyek---MTA Sz\'amit\'astechn. Automat. Kutato Int. Budapest},
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YEAR = {1976},
PAGES = {57--62},
MRCLASS = {65F20},
MRNUMBER = {57 \#4497}
}
@PREAMBLE{{\def\cprime{$'$} }}
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@PREAMBLE{{\def\cprime{$'$} }}
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MRNUMBER = {97h:65041}
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@PREAMBLE{{\def\cprime{$'$} }}
@ARTICLE{Galba97,
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@PREAMBLE{{\def\cprime{$'$} }}
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FJOURNAL = {Natsional\cprime naya Akademiya Nauk Ukrainy. Institut
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MRCLASS = {65F20},
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MRCLASS = {62J05},
MRNUMBER = {81m:62123},
KEYWORDS = {maximum likelihood estimation, Moore-Penrose},
NOTE = {(see \cite{Corradi82})}
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VOLUME = {33},
YEAR = {1980},
PAGES = {123--131},
MRCLASS = {15A09 (47A05)},
MRNUMBER = {82f:15003}
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@ARTICLE{GalperinWaksman98,
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ADDRESS = {New York}
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JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.},
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YEAR = {1966},
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@ARTICLE{Gay77,
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NUMBER = {140},
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VOLUME = {33},
YEAR = {1979},
NUMBER = {145},
PAGES = {432--433},
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MRNUMBER = {80g:65055}
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YEAR = {1996},
NUMBER = {2},
PAGES = {348--354},
MRCLASS = {15A23 (15A18 65F10)},
MRNUMBER = {96m:15023},
KEYWORDS = {Polar decomposition},
NOTE = {(see \cite{GeorgeIkramov97})}
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MRCLASS = {15A23 (15A18 65F10)},
MRNUMBER = {97m:15022}
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MRCLASS = {62J05 (65F30)},
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NOTE = {(Errata: ibid 4 (1975), no. 1, 81--82)}
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@BOOK{GetsonHsuan88,
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YEAR = {1988},
PAGES = {x+110},
ISBN = {0-387-96849-0},
MRCLASS = {15A09 (62H15 62J05)},
MRNUMBER = {90e:15004}
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JOURNAL = {An. Univ. Timi\c soara Ser. \c Sti. Mat.-Fiz. No.},
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YEAR = {1964},
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MRCLASS = {15.15},
MRNUMBER = {32 \#118}
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@BOOK{GlazmanLjubich69,
AUTHOR = {Glazman, I. M. and Ljubich, Ju. I.},
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PUBLISHER = {Nauka},
YEAR = {1969},
ADDRESS = {Moscow},
NOTE = {(English translation published by MIT Press)}
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@BOOK{Goldberg66,
AUTHOR = {Goldberg, S.},
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@ARTICLE{GoldmanZelen64,
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@BOOK{Goldstein67,
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VOLUME = {81},
YEAR = {1986},
PAGES = {207--236},
MRCLASS = {15A99},
MRNUMBER = {87k:15038}
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AUTHOR = {Golub, G. H.},
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PAGES = {206--216}
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@ARTICLE{Golub68,
AUTHOR = {Golub, G. H.},
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JOURNAL = {Aplikace Mathematiky},
YEAR = {1968},
VOLUME = {13},
PAGES = {44--51}
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@TECHREPORT{Golub69,
AUTHOR = {Golub, G. H.},
TITLE = {Matrix decompositions and statistical calculations},
INSTITUTION = {Stanford University},
YEAR = {1969},
TYPE = {Tech. Report},
NUMBER = {STAN-CS-124},
ADDRESS = {Stanford},
MONTH = {March}
}
@ARTICLE{GolubEtAl79,
AUTHOR = {Golub, G. H. and Heath, M. T. and Wahba, G.},
YEAR = {1979},
TITLE = {Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter},
JOURNAL = {Technometrics},
VOLUME = {21},
PAGES = {215--223}
}
@ARTICLE{GolubEtAl87,
AUTHOR = {Golub, G. H. and Hoffman, A. J. and Stewart, G. W.},
TITLE = {A generalization of the {E}ckart-{Y}oung-{M}irsky matrix approximation theorem},
JOURNAL = {Linear Algebra and its Applications},
FJOURNAL = {Linear Algebra and its Applications},
VOLUME = {88/89},
YEAR = {1987},
PAGES = {317--327},
MRCLASS = {41A45 (15A60 62J05 65F99)},
MRNUMBER = {88f:41039}
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@ARTICLE{GolubKahan65,
AUTHOR = {Golub, G. H. and Kahan, W.},
TITLE = {Calculating the singular values and pseudo-inverse of a matrix},
JOURNAL = {J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.},
VOLUME = {2},
YEAR = {1965},
PAGES = {205--224},
MRCLASS = {65.35},
MRNUMBER = {32 \#587},
NOTE = {(see \cite{DeMeersman70})}
}
@ARTICLE{GolubMeyer86,
AUTHOR = {Golub, G. H. and Meyer, Jr., C. D.},
TITLE = {Using the ${Q}{R}$ factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for {M}arkov chains},
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YEAR = {1986},
NUMBER = {2},
PAGES = {273--281},
MRCLASS = {60J10 (65F05)},
MRNUMBER = {87i:60073},
KEYWORDS = {appmar, approb}
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@ARTICLE{GolubPereyra73,
AUTHOR = {Golub, G. H. and Pereyra, V.},
YEAR = {1973},
TITLE = {The Differentiation of Pseudoinverses and Nonlinear Least Squares Problems Whose Variables Separate},
JOURNAL = {SIAM J. Numer. Anal.},
VOLUME = {10},
PAGES = {413--432},
KEYWORDS = {nlp, lsqnl, pert, mp, proj, lsq, matder}
}
@INPROCEEDINGS{GolubPereyra76,
AUTHOR = {Golub, G. H. and Pereyra, V.},
YEAR = {1976},
TITLE = {Differentiation of Pseudoinverses, Separable Nonlinear Least Squares Problems and Other Tales},
CROSSREF = {Nashed76},
PAGES = {303--324},
KEYWORDS = {nlp, lsqnl, pert, mp, proj, lsq, matder}
}
@ARTICLE{GolubReinsch70,
AUTHOR = {Golub, G. H. and Reinsch, C.},
YEAR = {1970},
TITLE = {Singular value decompositions and least squares solutions},
JOURNAL = {Numer. Math.},
VOLUME = {14},
PAGES = {403--420},
NOTE = {(republished, pp. 134--151 in \cite{WilkinsonReinsch71})},
KEYWORDS = {}
}
@ARTICLE{GolubStyan73,
AUTHOR = {Golub, G. H. and Styan, G. P. H.},
TITLE = {Numerical computations for univariate linear models},
JOURNAL = {Journal of Statistical Computations and Simulation},
YEAR = {1973},
VOLUME = {2},
PAGES = {253--274}
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@BOOK{GolubVanLoan96,
AUTHOR = {Golub, G. H. and Van Loan, C. F.},
TITLE = {Matrix {C}omputations},
EDITION = {Third},
PUBLISHER = {Johns Hopkins University Press},
ADDRESS = {Baltimore, MD},
YEAR = {1996},
PAGES = {xxx+698},
ISBN = {0-8018-5413-X; 0-8018-5414-8},
MRCLASS = {65-02 (65Fxx)},
MRNUMBER = {97g:65006}
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@ARTICLE{GolubWilkinson66,
AUTHOR = {G. H. Golub and J. H. Wilkinson},
YEAR = {1966},
TITLE = {Note on the iterative refinement of least squares solutions},
JOURNAL = {Numer. Math.},
VOLUME = {9},
PAGES = {139--148}
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@ARTICLE{GomezRomeu01,
AUTHOR = {G{\'o}mez, A. and Romeu, D.},
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PAGES = {551--556},
PUBLISHER = {Birkh\"auser Boston},
ADDRESS = {Boston, MA},
YEAR = {1990},
MRCLASS = {47A63 (15A60 47B15)},
MRNUMBER = {92k:47036}
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VOLUME = {137/138},
YEAR = {1990},
PAGES = {453--465},
MRCLASS = {47A63 (47B15 47D99 47N70 93B25)},
MRNUMBER = {91i:47020}
}
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AUTHOR = {Greville, T. N. E.},
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AUTHOR = {Greville, T. N. E.},
YEAR = {1966},
TITLE = {Note on the generalized inverse of a matrix product},
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@TECHREPORT{Greville67,
AUTHOR = {Greville, T. N. E.},
TITLE = {Spectral generalized inverses of square matrices},
INSTITUTION = {University of Wisconsin},
YEAR = {1967},
TYPE = {Math. Research Center Technical Summary Report},
NUMBER = {823},
ADDRESS = {Madison, WI},
MONTH = {October}
}
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AUTHOR = {Greville, T. N. E.},
CROSSREF = {BoullionOdell68},
TITLE = {Some new generalized inverses with spectral properties},
YEAR = {1968},
PAGES = {26--46}
}
@ARTICLE{Greville73,
AUTHOR = {Greville, T. N. E.},
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VOLUME = {6},
YEAR = {1973},
PAGES = {205--208},
MRCLASS = {15A09},
MRNUMBER = {47 \#237}
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PAGES = {828--832},
KEYWORDS = {proj, inv2}
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AUTHOR = {Greville, T. N. E. and Keyfitz, N.},
TITLE = {Backward population projection by a generalized inverse},
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PAGES = {173--183},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1980},
MRCLASS = {92A15 (15A09)},
MRNUMBER = {82b:92031}
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AUTHOR = {Griepentrog, E. and M{\"a}rz, R.},
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MRCLASS = {34A08},
MRNUMBER = {90d:34004}
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JOURNAL = {Canad. Math. Bull.},
VOLUME = {17},
YEAR = {1974},
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MRCLASS = {65J05 (47A50)},
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AUTHOR = {Groetsch, C. W.},
TITLE = {A product integral representation of the generalized inverse},
JOURNAL = {Comment. Math. Univ. Carolinae},
VOLUME = {16},
YEAR = {1975},
PAGES = {13--20},
MRCLASS = {47A60},
MRNUMBER = {52 \#11638}
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@ARTICLE{Groetsch75a,
AUTHOR = {Groetsch, C. W.},
TITLE = {Representations of the generalized inverse},
JOURNAL = {J. Math. Anal. Appl.},
VOLUME = {49},
YEAR = {1975},
PAGES = {154--157},
MRCLASS = {},
MRNUMBER = {50 \#14319}
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@BOOK{Groetsch77,
AUTHOR = {Groetsch, C. W.},
TITLE = {Generalized {I}nverses of {L}inear {O}perators: {R}epresentation and {A}pproximation. Monographs and Textbooks in Pure and Applied Mathematics, No.
37},
PUBLISHER = {Marcel Dekker Inc.},
ADDRESS = {New York},
YEAR = {1977},
PAGES = {viii+165},
MRCLASS = {65J05 (65F20)},
MRNUMBER = {56 \#17059}
}
@ARTICLE{Groetsch78,
AUTHOR = {Groetsch, C. W.},
TITLE = {The {F}orsythe-{M}otzkin method for singular linear operator equations},
JOURNAL = {J. Optim. Theory Appl.},
VOLUME = {25},
YEAR = {1978},
NUMBER = {2},
PAGES = {311--315},
MRCLASS = {65J05 (47A50)},
MRNUMBER = {58 \#8232}
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@ARTICLE{Groetsch79,
AUTHOR = {Groetsch, C. W.},
TITLE = {On rates of convergence for approximations to the generalized inverse},
JOURNAL = {Numer. Funct. Anal. Optim.},
FJOURNAL = {Numerical Functional Analysis and Optimization},
VOLUME = {1},
YEAR = {1979},
NUMBER = {2},
PAGES = {195--201},
MRCLASS = {65J10 (47A50)},
MRNUMBER = {80b:65072}
}
@ARTICLE{Groetsch80,
AUTHOR = {Groetsch, C. W.},
TITLE = {Generalized inverses and generalized splines},
JOURNAL = {Numer. Funct. Anal. Optim.},
FJOURNAL = {Numerical Functional Analysis and Optimization},
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YEAR = {1980},
NUMBER = {1},
PAGES = {93--97},
MRCLASS = {65J05 (47A05)},
MRNUMBER = {81j:65072},
KEYWORDS = {Splines, Hilbert},
NOTE = {(connection between generalized inverses and generalized splines, see \cite{Sard73})}
}
@BOOK{Groetsch84,
AUTHOR = {Groetsch, C. W.},
TITLE = {The {T}heory of {T}ikhonov {R}egularization for {F}redholm {E}quations of the {F}irst {K}ind},
PUBLISHER = {Pitman},
ADDRESS = {London},
YEAR = {1984},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{Groetsch92,
AUTHOR = {Groetsch, C. W.},
TITLE = {Spectral methods for linear inverse problems with unbounded operators},
JOURNAL = {J. Approx. Theory},
VOLUME = {70},
YEAR = {1992},
NUMBER = {1},
PAGES = {16--28},
MRCLASS = {47A50 (47A05 65J10)},
MRNUMBER = {93g:47011}
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@INCOLLECTION{Groetsch93,
AUTHOR = {Groetsch, C. W.},
TITLE = {Inclusions for the {M}oore-{P}enrose inverse with applications to computational methods},
BOOKTITLE = {Contributions in {N}umerical {M}athematics},
PAGES = {203--211},
PUBLISHER = {World Sci. Publishing},
ADDRESS = {River Edge, NJ},
YEAR = {1993},
MRCLASS = {65J20 (15A09 47A05 47A50)},
MRNUMBER = {95h:65041}
}
@BOOK{Groetsch93a,
AUTHOR = {Groetsch, C. W.},
TITLE = {Inverse {P}roblems in the {M}athematical {S}ciences},
PUBLISHER = {Friedr. Vieweg \& Sohn},
ADDRESS = {Braunschweig},
YEAR = {1993},
PAGES = {vi+152},
ISBN = {3-528-06545-1},
MRCLASS = {00A69 (35-02 35R25 35R30 45A05 47B07 65J20)},
MRNUMBER = {94m:00008}
}
@ARTICLE{Groetsch95,
AUTHOR = {Groetsch, C. W.},
TITLE = {Inclusions and identities for the {M}oore-{P}enrose inverse of a closed linear operator},
JOURNAL = {Math. Nachr.},
VOLUME = {171},
YEAR = {1995},
PAGES = {157--164},
MRCLASS = {47A05 (15A09)},
MRNUMBER = {96a:47004},
KEYWORDS = {spacH, invMP, linop}
}
@ARTICLE{GroetschGuacaneme87,
AUTHOR = {Groetsch, C. W. and Guacaneme, J.},
TITLE = {Arcangeli's method for {F}redholm equations of the first kind},
JOURNAL = {Proc. Amer. Math. Soc.},
VOLUME = {99},
YEAR = {1987},
NUMBER = {2},
PAGES = {256--260},
MRCLASS = {},
MRNUMBER = {88a:45016}
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@ARTICLE{GroetschHanke96,
AUTHOR = {Groetsch, C. W. and Hanke, M.},
TITLE = {A general framework for regularized evaluation of unstable operators},
JOURNAL = {J. Math. Anal. Appl.},
VOLUME = {203},
YEAR = {1996},
NUMBER = {2},
PAGES = {451--463},
MRCLASS = {},
MRNUMBER = {97f:65037}
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@INPROCEEDINGS{GroetschJacobs82,
AUTHOR = {Groetsch, C. W. and Jacobs, B. J.},
TITLE = {Iterative methods for generalized inverses based on functional interpolation},
CROSSREF = {Campbell82a},
PAGES = {220--232},
YEAR = {1982},
MRCLASS = {65J10 (47A05)},
MRNUMBER = {84c:65081},
KEYWORDS = {aprx, spacH, compit}
}
@ARTICLE{GroetschKing79,
AUTHOR = {Groetsch, C. W. and King, J. T.},
TITLE = {Extrapolation and the method of regularization for generalized inverses},
JOURNAL = {J. Approx. Theory},
VOLUME = {25},
YEAR = {1979},
NUMBER = {3},
PAGES = {233--247},
MRCLASS = {65J10 (47A05)},
MRNUMBER = {80e:65057}
}
@ARTICLE{GroetschNeubauer89,
AUTHOR = {Groetsch, C. W. and Neubauer, A.},
TITLE = {Regularization of ill-posed problems: optimal parameter choice in finite dimensions},
JOURNAL = {J. Approx. Theory},
VOLUME = {58},
YEAR = {1989},
NUMBER = {2},
PAGES = {184--200},
MRCLASS = {},
MRNUMBER = {90j:65083}
}
@ARTICLE{GroetschScherzer93,
AUTHOR = {Groetsch, C. W. and Scherzer, O.},
TITLE = {The optimal order of convergence for stable evaluation of differential operators},
JOURNAL = {Electronic J. Diff. Eqtns.},
VOLUME = {1993},
YEAR = {1993},
NUMBER = {4},
PAGES = {1--10},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{GroetschVogel87,
AUTHOR = {Groetsch, C. W. and Vogel, C. R.},
TITLE = {Asymptotic theory of filtering for linear operator equations with discrete noisy data},
JOURNAL = {Math. Comp.},
VOLUME = {49},
YEAR = {1987},
NUMBER = {180},
PAGES = {499--506},
MRCLASS = {},
MRNUMBER = {88j:65123}
}
@ARTICLE{Grone80,
AUTHOR = {Grone, R.},
TITLE = {Certain isometries of rectangular complex matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {29},
YEAR = {1980},
PAGES = {161--171},
MRCLASS = {15A60},
MRNUMBER = {81d:15007}
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AUTHOR = {Grone, R. and Johnson, C. R. and Sa, E. M. and Wolkowicz, H.},
TITLE = {Normal matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {87},
YEAR = {1987},
PAGES = {213--225},
MRCLASS = {15A57},
MRNUMBER = {88a:15045},
NOTE = {(characterizations of normal matrices, continued in \cite{ElsnerIkramov98})}
}
@ARTICLE{Gross97,
AUTHOR = {Gro{\ss}, J.},
TITLE = {Some remarks concerning the reverse order law},
JOURNAL = {Discuss. Math. Algebra Stochastic Methods},
FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods},
VOLUME = {17},
YEAR = {1997},
NUMBER = {2},
PAGES = {135--141},
MRCLASS = {15A09},
MRNUMBER = {99g:15004}
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@ARTICLE{Gross97a,
AUTHOR = {Gro{\ss}, J.},
TITLE = {Special generalized inverse matrices connected with the theory of unified least squares},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {264},
YEAR = {1997},
PAGES = {325--327},
MRCLASS = {62J05 (15A09)},
MRNUMBER = {1 465 874}
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@ARTICLE{Gross97b,
AUTHOR = {Gro{\ss}, J.},
TITLE = {A note on a partial ordering in the set of {H}ermitian matrices},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {18},
YEAR = {1997},
NUMBER = {4},
PAGES = {887--892},
MRCLASS = {15A57},
MRNUMBER = {98i:15027}
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@ARTICLE{Gross98,
AUTHOR = {Gro{\ss}, J.},
TITLE = {More on concavity of a matrix function},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {19},
YEAR = {1998},
NUMBER = {2},
PAGES = {365--368 (electronic)},
MRCLASS = {15A09 (15A45 62J12)},
MRNUMBER = {98m:15010}
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@ARTICLE{Gross98a,
AUTHOR = {Gro{\ss}, J.},
TITLE = {On contractions in linear regression},
JOURNAL = {J. Statist. Plann. Inference},
VOLUME = {74},
YEAR = {1998},
NUMBER = {2},
PAGES = {343--351},
MRCLASS = {62J05 (62C15)},
MRNUMBER = {2000c:62099}
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@ARTICLE{Gross99,
AUTHOR = {Gro{\ss}, J.},
TITLE = {Solution to a rank equation},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {289},
YEAR = {1999},
NUMBER = {1-3},
PAGES = {127--130},
MRCLASS = {15A24 (15A03)},
MRNUMBER = {99m:15011}
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@ARTICLE{Gross99a,
AUTHOR = {Gro{\ss}, J.},
TITLE = {Idempotency of the {H}ermitian part of a complex matrix},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {289},
YEAR = {1999},
NUMBER = {1-3},
PAGES = {135--139},
MRCLASS = {15A24 (15A57)},
MRNUMBER = {2000c:15017}
}
@ARTICLE{Gross99b,
AUTHOR = {Gro{\ss}, J.},
TITLE = {On the product of orthogonal projectors},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {289},
YEAR = {1999},
NUMBER = {1-3},
PAGES = {141--150},
MRCLASS = {15A21 (15A57)},
MRNUMBER = {99k:15023}
}
@ARTICLE{Gross99d,
AUTHOR = {Gro{\ss}, J.},
TITLE = {A note on the rank--subtractivity ordering},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {289},
YEAR = {1999},
NUMBER = {1-3},
PAGES = {151--160},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{Gross99c,
AUTHOR = {Gro{\ss}, J.},
TITLE = {On oblique projection, rank additivity and the {M}oore-{P}enrose inverse of the sum of two matrices},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {46},
YEAR = {1999},
NUMBER = {4},
PAGES = {265--275},
MRCLASS = {15A03 (15A09)},
MRNUMBER = {2000h:15002}
}
@ARTICLE{Gross00,
AUTHOR = {Gro{\ss}, J.},
TITLE = {The {M}oore-{P}enrose inverse of a partitioned nonnegative definite matrix},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {321},
YEAR = {2000},
NUMBER = {1-3},
PAGES = {113--121},
MRCLASS = {15A09 (15A48)},
MRNUMBER = {1 799 987}
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@ARTICLE{Gross01,
AUTHOR = {Gro{\ss}, J.},
TITLE = {Nonnegative-definite and positive-definite solutions to the matrix equation ${A}{X}{A}\sp \ast={B}$---revisited},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {321},
YEAR = {2000},
NUMBER = {1-3},
PAGES = {123--129},
MRCLASS = {15A24 (15A48)},
MRNUMBER = {1 799 988}
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@ARTICLE{Gross01a,
AUTHOR = {Gro{\ss}, J.},
TITLE = {L\"owner partial ordering and space preordering of {H}ermitian non-negative definite matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {326},
YEAR = {2001},
NUMBER = {1-3},
PAGES = {215--223},
MRCLASS = {15A48 (15A57 47A63)},
MRNUMBER = {1 815 961}
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@ARTICLE{GrossEtAl97,
AUTHOR = {Gro{\ss}, J. and Hauke, J. and Markiewicz, A.},
TITLE = {Some comments on matrix partial orderings},
JOURNAL = {Discuss. Math. Algebra Stochastic Methods},
FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods},
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}
@ARTICLE{Hartwig76,
AUTHOR = {Hartwig, R. E.},
TITLE = {Singular value decomposition and the {M}oore-{P}enrose inverse of bordered matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {31},
YEAR = {1976},
NUMBER = {1},
PAGES = {31--41},
MRCLASS = {15A09},
MRNUMBER = {53 \#10826},
KEYWORDS = {svd, invMP, matpar}
}
@ARTICLE{Hartwig76a,
AUTHOR = {Hartwig, R. E.},
TITLE = {More on the {S}ouriau-{F}rame algorithm and the {D}razin inverse},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {31},
YEAR = {1976},
NUMBER = {1},
PAGES = {42--46},
MRCLASS = {15A09},
MRNUMBER = {53 \#10827}
}
@ARTICLE{Hartwig76b,
AUTHOR = {Hartwig, R. E.},
TITLE = {Rank factorization and {M}oore-{P}enrose inversion},
JOURNAL = {Indust. Math.},
VOLUME = {26},
YEAR = {1976},
NUMBER = {1},
PAGES = {49--63},
MRCLASS = {15A09},
MRNUMBER = {53 \#5625}
}
@ARTICLE{Hartwig76c,
AUTHOR = {Hartwig, R. E.},
TITLE = {Block generalized inverses},
JOURNAL = {Arch. Rational Mech. Anal.},
VOLUME = {61},
YEAR = {1976},
NUMBER = {3},
PAGES = {197--251},
MRCLASS = {15A09 (16A28)},
MRNUMBER = {53 \#2975},
KEYWORDS = {matpar}
}
@ARTICLE{Hartwig77,
AUTHOR = {Hartwig, R. E.},
TITLE = {Generalized inverses of special block matrices},
JOURNAL = {Bull. Calcutta Math. Soc.},
FJOURNAL = {Bulletin of the Calcutta Mathematical Society},
VOLUME = {69},
YEAR = {1977},
NUMBER = {6},
PAGES = {397--402},
MRCLASS = {15A09},
MRNUMBER = {81a:15008}
}
@ARTICLE{Hartwig78,
AUTHOR = {Hartwig, R. E.},
TITLE = {Generalized inverses, ${E}{P}$ elements and associates},
JOURNAL = {Rev. Roumaine Math. Pures Appl.},
VOLUME = {23},
YEAR = {1978},
NUMBER = {1},
PAGES = {57--60},
MRCLASS = {15A33},
MRNUMBER = {57 \#12556}
}
@ARTICLE{Hartwig78a,
AUTHOR = {Hartwig, R. E.},
TITLE = {Spectral inverses and the row-space equations},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {20},
YEAR = {1978},
NUMBER = {1},
PAGES = {57--68},
MRCLASS = {15A09},
MRNUMBER = {57 \#6048},
KEYWORDS = {Drazin inverse, existence, properties}
}
@ARTICLE{Hartwig78b,
AUTHOR = {Hartwig, R. E.},
TITLE = {Schur's theorem and the {D}razin inverse},
JOURNAL = {Pacific J. Math.},
VOLUME = {78},
YEAR = {1978},
NUMBER = {1},
PAGES = {133--138},
MRCLASS = {15A09},
MRNUMBER = {80a:15004}
}
@ARTICLE{Hartwig78c,
AUTHOR = {Hartwig, R. E.},
TITLE = {A note on the partial ordering of positive semidefinite matrices},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {6},
YEAR = {1978},
PAGES = {223--226},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{Hartwig79,
AUTHOR = {Hartwig, R. E.},
TITLE = {A note on the existence of inner and outer inverses},
JOURNAL = {Math. Japon.},
FJOURNAL = {Mathematica Japonica},
VOLUME = {23},
YEAR = {1978/79},
NUMBER = {4},
PAGES = {339--343},
MRCLASS = {16A30 (16A32)},
MRNUMBER = {80g:16017}
}
@ARTICLE{Hartwig80,
AUTHOR = {Hartwig, R. E.},
TITLE = {How to partially order regular elements},
JOURNAL = {Math. Japon.},
VOLUME = {25},
YEAR = {1980},
NUMBER = {1},
PAGES = {1--13},
MRCLASS = {06F05},
MRNUMBER = {81i:06014}
}
@ARTICLE{Hartwig80a,
AUTHOR = {Hartwig, R. E.},
TITLE = {An application of the {M}oore-{P}enrose inverse to antisymmetric relations},
JOURNAL = {Proc. Amer. Math. Soc.},
VOLUME = {78},
YEAR = {1980},
NUMBER = {2},
PAGES = {181--186},
MRCLASS = {16A28 (15A09)},
MRNUMBER = {82a:16016}
}
@ARTICLE{Hartwig81,
AUTHOR = {Hartwig, R. E.},
TITLE = {A method for calculating ${A}\sp{d}$},
JOURNAL = {Math. Japon.},
VOLUME = {26},
YEAR = {1981},
NUMBER = {1},
PAGES = {37--43},
MRCLASS = {15A09},
MRNUMBER = {82h:15005}
}
@ARTICLE{Hartwig81a,
AUTHOR = {Hartwig, R. E.},
TITLE = {A note on rank additivity},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {10},
YEAR = {1981},
PAGES = {59--61},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{Hartwig81b,
AUTHOR = {Hartwig, R. E.},
TITLE = {Drazin inverses and canonical forms in ${M}\sb{n}({\bf {Z}}/h)$},
JOURNAL = {Linear Algebra and its Applications},
FJOURNAL = {Linear Algebra and its Applications},
VOLUME = {37},
YEAR = {1981},
PAGES = {205--233},
MRCLASS = {15A09 (15A36)},
MRNUMBER = {82k:15005}
}
@ARTICLE{Hartwig82,
AUTHOR = {Hartwig, R. E.},
TITLE = {Applications of the {W}ro\'nskian and {G}ram matrices of $\{t\sp{i}e\sp{\lambda \sb{k}t}\}$},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {43},
YEAR = {1982},
PAGES = {229--241},
MRCLASS = {93B05 (15A15 34A30 34H05)},
MRNUMBER = {83f:93007}
}
@ARTICLE{Hartwig86,
AUTHOR = {Hartwig, R. E.},
TITLE = {The reverse order law revisited},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {76},
YEAR = {1986},
PAGES = {241--246},
MRCLASS = {15A09},
MRNUMBER = {87j:15009}
}
@INCOLLECTION{Hartwig87,
AUTHOR = {Hartwig, R. E.},
TITLE = {The group inverse of a block triangular matrix},
BOOKTITLE = {Current {T}rends in {M}atrix {T}heory ({A}uburn,
{A}la., 1986)},
PAGES = {137--146},
PUBLISHER = {North-Holland},
ADDRESS = {New York},
YEAR = {1987},
MRCLASS = {15A09 (15A57)},
KEYWORDS = {invgr, strm},
MRNUMBER = {88f:15007}
}
@ARTICLE{Hartwig87a,
AUTHOR = {Hartwig, R. E.},
TITLE = {A remark on the characterization of the parallel sum of two matrices},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {22},
YEAR = {1987},
NUMBER = {2},
PAGES = {193--197},
MRCLASS = {15A09 (15A30 15A33)},
MRNUMBER = {89f:15006}
}
@ARTICLE{Hartwig93,
AUTHOR = {Hartwig, R. E.},
TITLE = {The pyramid decomposition and rank minimization},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {191},
YEAR = {1993},
PAGES = {53--76},
MRCLASS = {15A23},
MRNUMBER = {94j:15011}
}
@ARTICLE{Hartwig94,
AUTHOR = {Hartwig, R. E.},
TITLE = {The weighted $*$-core-nilpotent decomposition},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {211},
YEAR = {1994},
PAGES = {101--111},
MRCLASS = {15A09 (15A21)},
MRNUMBER = {95i:15004}
}
@ARTICLE{Hartwig94a,
AUTHOR = {Hartwig, R. E.},
TITLE = {E{P} perturbations},
JOURNAL = {Sankhy\=a Ser. A},
FJOURNAL = {Sankhy\=a. The Indian Journal of Statistics. Series A},
VOLUME = {56},
YEAR = {1994},
NUMBER = {2},
PAGES = {347--357},
MRCLASS = {15A57 (15A09)},
MRNUMBER = {99j:15033}
}
@ARTICLE{HartwigDrazin82,
AUTHOR = {Hartwig, R. E. and Drazin, M. P.},
TITLE = {Lattice properties of the * order for matrices},
JOURNAL = {J. Math. Anal. Appl.},
VOLUME = {86},
YEAR = {1982},
PAGES = {359--378}
}
@ARTICLE{HartwigHall78,
AUTHOR = {Hartwig, R. E. and Hall, F. J.},
TITLE = {Pseudo--similarity for matrices over a field},
JOURNAL = {Proc. Amer. Math. Soc.},
VOLUME = {71},
YEAR = {1978},
NUMBER = {1},
PAGES = {6--10},
MRCLASS = {15A21},
MRNUMBER = {58 \#28027}
}
@INPROCEEDINGS{HartwigHall82,
AUTHOR = {Hartwig, R. E. and Hall, F. J.},
TITLE = {Applications of the {D}razin inverse to {C}es\`aro--{N}eumann iterations},
CROSSREF = {Campbell82a},
PAGES = {145--195},
YEAR = {1982},
MRCLASS = {15A09},
MRNUMBER = {84a:15006},
KEYWORDS = {invD, compit, serexp}
}
@ARTICLE{HartwigKatz97,
AUTHOR = {Hartwig, R. E. and Katz, I. J.},
TITLE = {On products of {E}{P} matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {252},
YEAR = {1997},
PAGES = {339--345},
MRCLASS = {15A57},
MRNUMBER = {98a:15050}
}
@ARTICLE{HartwigLevine81,
AUTHOR = {Hartwig, R. E. and Levine, J.},
TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {III}},
JOURNAL = {Cryptologia},
VOLUME = {5},
YEAR = {1981},
NUMBER = {2},
PAGES = {67--77},
MRCLASS = {94B99},
MRNUMBER = {82j:94022a}
}
@ARTICLE{HartwigLevine81a,
AUTHOR = {Hartwig, R. E. and Levine, J.},
TITLE = {Applications of the {D}razin inverse to the {H}ill cryptographic system. {IV}},
JOURNAL = {Cryptologia},
VOLUME = {5},
YEAR = {1981},
NUMBER = {4},
PAGES = {213--228},
MRCLASS = {94B99},
MRNUMBER = {82j:94022b}
}
@ARTICLE{HartwigLuh77,
AUTHOR = {Hartwig, R. E. and Luh, Jiang},
TITLE = {A note on the group structure of unit regular ring elements},
JOURNAL = {Pacific J. Math.},
VOLUME = {71},
YEAR = {1977},
NUMBER = {2},
PAGES = {449--461},
MRCLASS = {16A30},
MRNUMBER = {56 \#407},
KEYWORDS = {algr}
}
@ARTICLE{HartwigLuh81,
AUTHOR = {Hartwig, R. E. and Luh, Jiang},
TITLE = {Unitary regular rings and partial isometry rings},
JOURNAL = {Math. Japon.},
FJOURNAL = {Mathematica Japonica},
VOLUME = {26},
YEAR = {1981},
NUMBER = {4},
PAGES = {401--413},
MRCLASS = {16A30 (16A28)},
MRNUMBER = {83b:16008}
}
@ARTICLE{HartwigSemrl99,
AUTHOR = {Hartwig, R. E. and {\v{S}}emrl, P.},
TITLE = {Power additivity and orthogonality},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
FJOURNAL = {SIAM Journal on Matrix Analysis and Applications},
VOLUME = {20},
YEAR = {1999},
NUMBER = {1},
PAGES = {1--13 (electronic)},
MRCLASS = {15A21 (15A24)},
MRNUMBER = {99f:15016}
}
@ARTICLE{HartwigShoaf77,
AUTHOR = {Hartwig, R. E. and Shoaf, J. M.},
TITLE = {Group inverses and {D}razin inverses of bidiagonal and triangular {T}oeplitz matrices},
JOURNAL = {J. Austral. Math. Soc. Ser. A},
VOLUME = {24},
YEAR = {1977},
NUMBER = {1},
PAGES = {10--34},
MRCLASS = {15A09},
MRNUMBER = {57 \#3150},
KEYWORDS = {invD, invgr}
}
@ARTICLE{HartwigShoaf79,
AUTHOR = {Hartwig, R. E. and Shoaf, J. M.},
TITLE = {On the derivative of the {D}razin inverse of a complex matrix},
JOURNAL = {SIAM J. Math. Anal.},
VOLUME = {10},
YEAR = {1979},
NUMBER = {1},
PAGES = {207--216},
MRCLASS = {65F20 (15A09)},
MRNUMBER = {80b:65050}
}
@ARTICLE{HartwigShoaf80,
AUTHOR = {Hartwig, R. E. and Shoaf, J. M.},
TITLE = {Invariance, group inverses and parallel sums},
JOURNAL = {Rev. Roumaine Math. Pures Appl.},
FJOURNAL = {Acad\'emie de la R\'epublique Populaire Roumaine. Revue
Roumaine de Math\'ematiques Pures et Appliqu\'ees},
VOLUME = {25},
YEAR = {1980},
NUMBER = {1},
PAGES = {33--42},
MRCLASS = {16A30},
MRNUMBER = {82e:16007}
}
@ARTICLE{HartwigStyan86,
AUTHOR = {Hartwig, R. E. and Styan, G. P. H.},
TITLE = {On some characterizations of the star partial orderings and rank subtractivity},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {82},
YEAR = {1986},
PAGES = {145--161},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{HartwigEtAl96,
AUTHOR = {Hartwig, R. E. and Omladi{\v{c}}, M. and {\v{S}}emrl, P. and Styan, G. P. H.},
TITLE = {On some characterizations of pairwise star ortogonality using rank and dagger additivity and subtractivity},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {237--238},
YEAR = {1996},
PAGES = {499--507},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{HartwigEtAl01,
AUTHOR = {Hartwig, R. E. and Wang, Guorong and Wei, Yimin},
TITLE = {Some additive results on {D}razin inverse},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {322},
YEAR = {2001},
NUMBER = {1-3},
PAGES = {207--217},
MRCLASS = {15A09},
MRNUMBER = {1 804 521}
}
@ARTICLE{Harville76,
AUTHOR = {Harville, D. A.},
TITLE = {Extension of the {G}auss-{M}arkov theorem to include the estimation of random effects},
JOURNAL = {Ann. Statist.},
VOLUME = {4},
YEAR = {1976},
NUMBER = {2},
PAGES = {384--395},
MRCLASS = {62J05},
MRNUMBER = {53 \#1862}
}
@ARTICLE{Harville96,
AUTHOR = {Harville, D. A.},
TITLE = {Generalized inverses and ranks of modified matrices},
JOURNAL = {J. Indian Soc. Agricultural Statist.},
VOLUME = {49},
YEAR = {1996/97},
PAGES = {67--78, iv},
MRCLASS = {15A09},
MRNUMBER = {98f:15001}
}
@BOOK{Harville97,
AUTHOR = {Harville, D. A.},
TITLE = {Matrix {A}lgebra from a {S}tatistician's {P}erspective},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1997},
PAGES = {xviii+630},
ISBN = {0-387-94978-X},
MRCLASS = {15-01},
MRNUMBER = {98k:15001}
}
@ARTICLE{HarwoodEtAl70,
AUTHOR = {Harwood, W. R. and Lovass--Nagy, V. and Powers, D. L.},
TITLE = {A note on the generalized inverses of some partitioned matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {19},
YEAR = {1970},
PAGES = {555--559},
MRCLASS = {65.35 (15.00)},
MRNUMBER = {42 \#7048}
}
@ARTICLE{Haussler78,
AUTHOR = {H{\"a}ussler, W. M.},
TITLE = {Zu \"uber- und unterrelaxierten {N}ewton-{V}erfahren},
JOURNAL = {Z. Angew. Math. Mech.},
FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik.
Ingenieurwissenschaftliche Forschungsarbeiten},
VOLUME = {58},
YEAR = {1978},
NUMBER = {7},
PAGES = {T421--T423},
MRCLASS = {65H05},
MRNUMBER = {80g:65053}
}
@ARTICLE{HawkinsBradu90,
AUTHOR = {Hawkins, D. M. and Bradu, D.},
TITLE = {Application of the {M}oore-{P}enrose inverse of a data matrix in multiple regression},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {127},
YEAR = {1990},
PAGES = {403--425},
MRCLASS = {62J05 (62J20)},
MRNUMBER = {91f:62117}
}
@ARTICLE{HawkinsBen-Israel73,
AUTHOR = {Hawkins, J. B. and Ben-Israel, A.},
TITLE = {On generalized matrix functions},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {1},
YEAR = {1973},
NUMBER = {2},
PAGES = {163--171},
MRCLASS = {15A15},
MRNUMBER = {48 \#8523},
KEYWORDS = {matfun}
}
@ARTICLE{Haynsworth70,
AUTHOR = {Haynsworth, E. V.},
TITLE = {Applications of an inequality for the {S}chur complement},
JOURNAL = {Proc. Amer. Math. Soc.},
VOLUME = {24},
YEAR = {1970},
PAGES = {512--516},
KEYWORDS = {Schur complement}
}
@ARTICLE{HaynsworthWall79,
AUTHOR = {Haynsworth, E. V. and Wall, J. R.},
TITLE = {Group inverses of certain nonnegative matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {25},
YEAR = {1979},
PAGES = {271--288},
MRCLASS = {15A09},
MRNUMBER = {80b:15006}
}
@ARTICLE{HaynsworthWall81,
AUTHOR = {Haynsworth, E. V. and Wall, J. R.},
TITLE = {Group inverses of certain positive operators},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {40},
YEAR = {1981},
PAGES = {143--159},
MRCLASS = {15A09 (15A48)},
MRNUMBER = {82j:15004}
}
@ARTICLE{HaukeMarkiewicz95,
AUTHOR = {Hauke, J. and Markiewicz, A.},
TITLE = {On partial orderings on the set of rectangular matrices and their properties},
JOURNAL = {Discuss. Math. Algebra Stochastic Methods},
FJOURNAL = {Discussiones Mathematicae. Algebra and Stochastic Methods},
VOLUME = {15},
YEAR = {1995},
NUMBER = {1},
PAGES = {5--10},
MRCLASS = {15A99},
MRNUMBER = {96k:15018},
KEYWORDS = {Partial orders, matrix functions}
}
@ARTICLE{HaukeMarkiewicz95a,
AUTHOR = {Hauke, J. and Markiewicz, A.},
TITLE = {On partial orderings on the set of rectangular matrices},
JOURNAL = {Linear Algebra and its Applications},
FJOURNAL = {Linear Algebra and its Applications},
VOLUME = {219},
YEAR = {1995},
PAGES = {187--193},
MRCLASS = {15A48},
MRNUMBER = {96c:15033},
KEYWORDS = {Partial orders, matrix functions},
NOTE = {(see \cite{Markiewicz99})}
}
@ARTICLE{Hearon67,
AUTHOR = {Hearon, J. Z.},
TITLE = {On the singularity of a certain bordered matrix},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {15},
YEAR = {1967},
PAGES = {1413--1421},
MRCLASS = {15.15},
MRNUMBER = {37 \#225}
}
@ARTICLE{Hearon67a,
AUTHOR = {Hearon, J. Z.},
TITLE = {Polar factorization of a matrix},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {71B},
YEAR = {1967},
PAGES = {65--67},
MRCLASS = {15.15},
MRNUMBER = {37 \#1382}
}
@ARTICLE{Hearon67aa,
AUTHOR = {Hearon, J. Z.},
TITLE = {Construction of ${\rm {E}{P}r}$ generalized inverses by inversion of nonsingular matrices},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {71B},
YEAR = {1967},
PAGES = {57--60},
MRCLASS = {15.15 (65.00)},
MRNUMBER = {36 \#6425}
}
@ARTICLE{Hearon67aaa,
AUTHOR = {Hearon, J. Z.},
TITLE = {A generalized matrix version of {R}ennie's inequality},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {71B},
YEAR = {1967},
PAGES = {61--64},
MRCLASS = {15.58},
MRNUMBER = {37 \#232}
}
@ARTICLE{Hearon67b,
AUTHOR = {Hearon, J. Z.},
TITLE = {Partially isometric matrices},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {71B},
YEAR = {1967},
PAGES = {225--228},
MRCLASS = {15.30},
MRNUMBER = {37 \#2779}
}
@ARTICLE{Hearon67c,
AUTHOR = {Hearon, J. Z.},
TITLE = {Symmetrizable generalized inverses of symmetrizable matrices},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {71B},
YEAR = {1967},
PAGES = {229--231},
MRCLASS = {15.15},
MRNUMBER = {37 \#2770}
}
@ARTICLE{Hearon68,
AUTHOR = {Hearon, J. Z.},
TITLE = {Generalized inverses and solutions of linear systems},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {72B},
YEAR = {1968},
PAGES = {303--308},
MRCLASS = {15.15},
MRNUMBER = {39 \#224}
}
@ARTICLE{HearonEvans68,
AUTHOR = {Hearon, J. Z. and Evans, J. W.},
TITLE = {On spaces and maps of generalized inverses},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {72B},
YEAR = {1968},
PAGES = {103--107},
MRCLASS = {15.15},
MRNUMBER = {38 \#4493}
}
@ARTICLE{HearonEvans68a,
AUTHOR = {Hearon, J. Z. and Evans, J. W.},
TITLE = {Differentiable generalized inverses},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {72B},
YEAR = {1968},
PAGES = {109--113},
MRCLASS = {15.15},
KEYWORDS = {alglin, pert, invMP, matder},
MRNUMBER = {38 \#4494}
}
@ARTICLE{Hedman99,
AUTHOR = {Hedman, B. A.},
TITLE = {An earlier date for ``{C}ramer's rule''},
JOURNAL = {Historia Math.},
FJOURNAL = {Historia Mathematica},
VOLUME = {26},
YEAR = {1999},
NUMBER = {4},
PAGES = {365--368},
MRCLASS = {01A50},
MRNUMBER = {2000i:01020},
NOTE = {(Cramer's rule was discovered by Maclaurin 20 years earlier)}
}
@ARTICLE{HeilWalnut89,
AUTHOR = {Heil, C. and Walnut, D.},
TITLE = {Continuous and discrete wavelet transforms},
JOURNAL = {SIAM Rev.},
VOLUME = {31},
YEAR = {1989},
PAGES = {628--666},
MRCLASS = {},
MRNUMBER = {91c:42032}
}
@ARTICLE{Heinig97,
AUTHOR = {Heinig, G.},
TITLE = {The group inverse of the transformation ${S}({X})={A}{X}-{X}{B}$},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {257},
YEAR = {1997},
PAGES = {321--342},
MRCLASS = {15A09 (15A04)},
MRNUMBER = {98c:15014}
}
@ARTICLE{HeinigHellinger93,
AUTHOR = {Heinig, G. and Hellinger, F.},
TITLE = {On the {Bezoutian} Structure of the {Moore--Penrose} Inverses of {Hankel} Matrices},
JOURNAL = {SIAM Journal on Matrix Analysis and Applications},
VOLUME = {14},
NUMBER = {3},
PAGES = {629--645},
YEAR = {1993},
MRCLASS = {15A09 (15A57 47A05 47B35)},
MRNUMBER = {94f:15006}
}
@ARTICLE{HeinigHellinger93a,
AUTHOR = {Heinig, G. and Hellinger, F.},
TITLE = {Displacement structure of generalized inverse matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {211},
YEAR = {1994},
PAGES = {67--83},
MRCLASS = {15A09 (65F20)},
MRNUMBER = {95h:15006}
}
@ARTICLE{HeinigHellinger94,
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YEAR = {1994},
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VOLUME = {197/198},
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MRNUMBER = {95h:15006}
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AUTHOR = {Homeier, H. H. H.},
TITLE = {{The vector ${\mathcal{J}}$ extrapolation method}},
BOOKTITLE = {{Iterative {M}ethods in {S}cientific {C}omputation}},
EDITOR = { Junping Wang and Allen, {III.}, Myron B. and Chen, Benito
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NOTE = {Proceedings of the {\em Third IMACS International
Symposium on Iterative Methods in Scientific Computation
Jackson Hole, Wyoming, USA - July 9-12, 1997}},
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VOLUME = 4,
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SERIES = {IMACS Series in Computational and Applied Mathematics},
PUBLISHER = {IMACS, Dept. of Computer Science, Rutgers University, New
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ISSN = {1098-870X},
TECH = {Technical Report TC-NA-97-5, Institut f{\"u}r
{P}hysikalische und {T}heoretische {C}hemie,
{U}niversit{\"a}t {R}egensburg, {D}-93040 {R}egensburg,
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PAGES = {39--54},
PUBLISHER = {Springer},
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YEAR = {1963}
}
@ARTICLE{Kaltenbacher97,
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JOURNAL = {Applicable Anal.},
VOLUME = {1},
YEAR = {1971},
NUMBER = {2},
PAGES = {143--159},
MRCLASS = {47.10 (65.00)},
MRNUMBER = {44 \#7319}
}
@ARTICLE{KammererNashed71a,
AUTHOR = {Kammerer, W. J. and Nashed, M. Z.},
TITLE = {A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind},
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VOLUME = {51},
YEAR = {1971},
PAGES = {20--25}
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@ARTICLE{KammererNashed72,
AUTHOR = {Kammerer, W. J. and Nashed, M. Z.},
TITLE = {Iterative methods for best approximate solutions of linear integral equations of the first and second kinds},
JOURNAL = {J. Math. Anal. Appl.},
VOLUME = {40},
YEAR = {1972},
PAGES = {547--573}
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AUTHOR = {Kammerer, W. J. and Nashed, M. Z.},
TITLE = {On the convergence of the conjugate gradient method for singular linear operator equations},
JOURNAL = {SIAM J. Numer. Anal.},
VOLUME = {9},
YEAR = {1972},
PAGES = {165--181}
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@BOOK{KantorovichAkilov64,
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TITLE = {Functional {A}nalysis in {N}ormed {S}paces},
PUBLISHER = {Pergamon Press},
YEAR = {1964},
ADDRESS = {Oxford},
NOTE = {(translated from Russian)}
}
@BOOK{KantorovichKrylov58,
AUTHOR = {Kantorovich, L. V. and Krylov, V. I.},
TITLE = {Approximate {M}ethods of {H}igher {A}nalysis},
PUBLISHER = {Interscience},
YEAR = {1958},
ADDRESS = {New York},
NOTE = {(translated from Russian)}
}
@ARTICLE{Karampetakis97,
AUTHOR = {Karampetakis, N. P.},
TITLE = {Computation of the generalized inverse of a polynomial matrix and applications},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {252},
YEAR = {1997},
PAGES = {35--60},
MRCLASS = {65F20 (93C05)},
MRNUMBER = {98c:65066}
}
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AUTHOR = {Karampetakis, N. P.},
TITLE = {Generalized inverses of two-variable polynomial matrices and applications},
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FJOURNAL = {Circuits, Systems, and Signal Processing},
VOLUME = {16},
YEAR = {1997},
NUMBER = {4},
PAGES = {439--453},
MRCLASS = {15A09 (39B42 65F20 93C35)},
MRNUMBER = {98i:15008}
}
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AUTHOR = {Karasalo, I.},
TITLE = {A criterion for truncation of the ${Q}{R}$-decomposition algorithm for the singular linear least squares problem},
JOURNAL = {Nordisk Tidskr. Informationsbehandling (BIT)},
VOLUME = {14},
YEAR = {1974},
PAGES = {156--166},
MRCLASS = {65F20},
MRNUMBER = {58 \#3372}
}
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AUTHOR = {Kass, S.},
TITLE = {Spaces of closest fit},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {117},
YEAR = {1989},
PAGES = {93--97},
MRCLASS = {51K05 (15A03 15A99)},
MRNUMBER = {90f:51018}
}
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AUTHOR = {Kato, Yoshinobu and Moriya, Nobuhiro},
TITLE = {Maeda's inequality for pseudoinverses},
JOURNAL = {Math. Japon.},
VOLUME = {22},
YEAR = {1977},
NUMBER = {1},
PAGES = {89--91},
MRCLASS = {47A30},
MRNUMBER = {56 \#6434},
MRREVIEWER = {Chandler Davis}
}
@ARTICLE{KatsaggelosEfstratiadis90,
AUTHOR = {Katsaggelos, A. K. and Efstratiadis, S. N.},
TITLE = {A class of iterative signal restoration algorithms},
JOURNAL = {IEEE Trans. Acoust. Speech Signal Process.},
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VOLUME = {38},
YEAR = {1990},
NUMBER = {5},
PAGES = {778--786},
MRCLASS = {94A12 (65F05)},
MRNUMBER = {91f:94006},
KEYWORDS = {appvis}
}
@ARTICLE{Katz65,
AUTHOR = {Katz, I. J.},
TITLE = {Wiegmann type theorems for {$EP_r$} matrices},
JOURNAL = {Duke Math. J.},
YEAR = {1965},
VOLUME = {32},
PAGES = {423--427}
}
@ARTICLE{Katz70,
AUTHOR = {Katz, I. J.},
TITLE = {Remarks on a paper of {B}en-{I}srael},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {18},
YEAR = {1970},
PAGES = {511--513},
MRCLASS = {15.10},
MRNUMBER = {41 \#6863}
}
@ARTICLE{KatzPearl66,
AUTHOR = {Katz, I. J. and Pearl, M. H.},
TITLE = {On ${E}{P}r$ and normal ${E}{P}r$ matrices},
JOURNAL = {J. Res. Nat. Bur. Standards Sect. B},
VOLUME = {70B},
YEAR = {1966},
PAGES = {47--77},
MRCLASS = {15.30},
MRNUMBER = {33 \#7358},
KEYWORDS = {matEP}
}
@ARTICLE{KatzPearl66a,
AUTHOR = {Katz, I. J. and Pearl, M. H.},
TITLE = {Solutions of the matrix equation ${A}\sp{\ast}
={X}{A}={A}{X}$},
JOURNAL = {J. London Math. Soc.},
VOLUME = {41},
YEAR = {1966},
PAGES = {443--452},
MRCLASS = {15.35},
MRNUMBER = {33 \#4072}
}
@ARTICLE{KaufmanPereyra78,
AUTHOR = {Kaufman, L. and Pereyra, V.},
TITLE = {A method for separable nonlinear least squares problems with separable nonlinear equality constraints},
JOURNAL = {SIAM J. Numer. Anal.},
VOLUME = {15},
YEAR = {1978},
NUMBER = {1},
PAGES = {12--20},
MRCLASS = {90C30},
MRNUMBER = {57 \#11766},
KEYWORS = {Nonlinear least squares}
}
@ARTICLE{Keller65,
AUTHOR = {H. B. Keller},
YEAR = {1965},
TITLE = {On the Solution of Singular and Semidefinite Linear Systems by Iteration},
JOURNAL = {SIAM Journal on Numerical Analysis},
VOLUME = {2},
PAGES = {281--290},
KWDS = {nla, linear system, iter, singular system}
}
@ARTICLE{Keller-McNultyKennedy87,
AUTHOR = {Keller-McNulty, S. and Kennedy, W. J.},
TITLE = {Error-free computation of the {M}oore-{P}enrose inverse with application to linear least squares analysis},
JOURNAL = {J. Statist. Comput. Simulation},
VOLUME = {27},
YEAR = {1987},
NUMBER = {1},
PAGES = {45--64},
MRCLASS = {65F20 (65D10 65U05)},
MRNUMBER = {90a:65093}
}
@ARTICLE{Kelly98,
AUTHOR = {Kelly, J. D.},
TITLE = {A regularization approach to the reconciliation of constrained data sets},
JOURNAL = {Computers \& Chemical Engineering},
VOLUME = {22},
YEAR = {1998},
PAGES = {1771--1788}
}
@ARTICLE{Khabaza63,
AUTHOR = {Khabaza, I. M.},
TITLE = {An iterative least-square method suitable for solving large sparse matrices},
JOURNAL = {Comput. J.},
VOLUME = {6},
YEAR = {1963/1964},
PAGES = {202--206},
MRCLASS = {65.35},
MRNUMBER = {27 \#4351}
}
@INCOLLECTION{KhajdukovEtAl97,
AUTHOR = {Khajdukov, V. G. and Kostin, V. I. and Tcheverda, V. A.},
TITLE = {The $r$-solution and its applications in linearized waveform inversion for a layered background},
BOOKTITLE = {Inverse {P}roblems in {W}ave {P}ropagation ({M}inneapolis, {MN}, 1995)},
PAGES = {277--294},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1997},
MRCLASS = {35R30 (35L05 65M12 76Q05)},
MRNUMBER = {98j:35185}
}
@ARTICLE{Khatri67,
AUTHOR = {Khatri, C. G.},
TITLE = {A theorem on least squares in multivariate linear regression},
JOURNAL = {J. Amer. Statist. Assoc.},
VOLUME = {62},
YEAR = {1967},
PAGES = {1494--1495},
MRCLASS = {},
MRNUMBER = {36 \#3464}
}
@ARTICLE{Khatri69,
AUTHOR = {Khatri, C. G.},
TITLE = {A note on some results on a generalised inverse of a matrix},
JOURNAL = {J. Indian Statist. Assoc.},
VOLUME = {7},
YEAR = {1969},
PAGES = {38--45},
MRCLASS = {},
MRNUMBER = {48 \#3980}
}
@ARTICLE{Khatri70,
AUTHOR = {Khatri, C. G.},
TITLE = {A note on a commutative $g$-inverse of a matrix},
JOURNAL = {Sankhy\=a Ser. A},
VOLUME = {32},
YEAR = {1970},
PAGES = {299--310},
MRCLASS = {15A09},
MRNUMBER = {45 \#1939}
}
@ARTICLE{Khatri82,
AUTHOR = {Khatri, C. G.},
TITLE = {A representation of a matrix and its use in the {G}auss-{M}arkoff model},
JOURNAL = {J. Indian Statist. Assoc.},
VOLUME = {20},
YEAR = {1982},
PAGES = {89--98},
MRCLASS = {62J05 (62F10)},
MRNUMBER = {86k:62115}
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@ARTICLE{Khatri83,
AUTHOR = {Khatri, C. G.},
TITLE = {A generalization of {L}avoie's inequality concerning the sum of idempotent matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {54},
YEAR = {1983},
PAGES = {97--108},
MRCLASS = {15A09 (15A18)},
MRNUMBER = {85i:15006}
}
@ARTICLE{Khatri85,
AUTHOR = {Khatri, C. G.},
TITLE = {A note on idempotent matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {70},
YEAR = {1985},
PAGES = {185--195},
MRCLASS = {15A57 (15A09)},
MRNUMBER = {87d:15019}
}
@ARTICLE{Khatri85a,
AUTHOR = {Khatri, C. G.},
TITLE = {Commutative $g$-inverse of a matrix},
JOURNAL = {Math. Today},
FJOURNAL = {Mathematics Today},
VOLUME = {3},
YEAR = {1985},
PAGES = {37--40},
MRCLASS = {15A09},
MRNUMBER = {87b:15006}
}
@ARTICLE{Khatri89,
AUTHOR = {Khatri, C. G.},
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JOURNAL = {Comm. Statist. Theory Methods},
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VOLUME = {18},
YEAR = {1989},
NUMBER = {4},
PAGES = {1425--1440},
MRCLASS = {62H20},
MRNUMBER = {91b:62114}
}
@ARTICLE{KhatriMitra76,
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TITLE = {Hermitian and nonnegative solutions of linear matrix equations},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {31},
YEAR = {1976},
PAGES = {579--585}
}
@ARTICLE{KhatriRao81,
AUTHOR = {Khatri, C. G. and Rao, C. R.},
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JOURNAL = {J. Multivariate Anal.},
VOLUME = {11},
YEAR = {1981},
NUMBER = {4},
PAGES = {498--505},
MRCLASS = {15A15 (15A45 62J05)},
MRNUMBER = {84e:15006}
}
@INCOLLECTION{Kiekebusch-Muller77,
AUTHOR = {Kiekebusch-M{\"u}ller, B. D.},
TITLE = {A class of algorithms for the determination of a solution of a system of nonlinear equations},
BOOKTITLE = {Optimization {T}echniques ({P}roc. 8th {IFIP} {C}onf., {W}{\"u}rzburg,
1977), {P}art 2},
PAGES = {67--75. Lecture Notes in Control and Informat. Sci., Vol. 7},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
MRCLASS = {65H10},
MRNUMBER = {58 \#13678}
}
@ARTICLE{KimLee86,
AUTHOR = {Kim, Byung Chun and Lee, Jang Taek},
TITLE = {The {M}oore-{P}enrose inverse for the classificatory models},
JOURNAL = {J. Korean Statist. Soc.},
VOLUME = {15},
YEAR = {1986},
NUMBER = {1},
PAGES = {46--61},
MRCLASS = {15A09 (15A06 62J10)},
MRNUMBER = {87m:15012}
}
@ARTICLE{KimOh99,
AUTHOR = {Kim, Doh-Hyun and Oh, Jun-Ho},
TITLE = {The {M}oore-{P}enrose inverse for the classificatory models},
JOURNAL = {Control Engineering Practice},
VOLUME = {7},
YEAR = {1999},
NUMBER = {3},
PAGES = {369--373}
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@ARTICLE{KimS98,
AUTHOR = {Kim, S.},
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VOLUME = {13},
YEAR = {1998},
NUMBER = {4},
PAGES = {875--888},
MRCLASS = {65R32},
MRNUMBER = {2000i:65223}
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@ARTICLE{KimS98a,
AUTHOR = {Kim, S.},
TITLE = {Solving singular integral equations using {G}aussian quadrature and overdetermined system},
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VOLUME = {35},
YEAR = {1998},
NUMBER = {10},
PAGES = {63--71},
MRCLASS = {65R20 (65D32)},
MRNUMBER = {99b:65175}
}
@ARTICLE{KimS99,
AUTHOR = {Kim, S.},
TITLE = {Numerical Solutions of Cauchy Singular Integral Equations Using Generalized Inverses},
JOURNAL = {Computers \& Mathematics with Applications},
VOLUME = {38},
YEAR = {1999},
NUMBER = {5--6},
PAGES = {183--195}
}
@ARTICLE{King77,
AUTHOR = {King, Chen F.},
TITLE = {A note on {D}razin inverses},
JOURNAL = {Pacific J. Math.},
VOLUME = {70},
YEAR = {1977},
NUMBER = {2},
PAGES = {383--390},
MRCLASS = {47B30 (47A05)},
MRNUMBER = {58 \#2418}
}
@PHDTHESIS{Kirby65,
AUTHOR = {Kirby, M. J. L.},
TITLE = {Generalized {I}nverses and {C}hance {C}onstrained {P}rogramming},
SCHOOL = {Northwestern Univ.},
YEAR = {1965},
TYPE = {Applied Math.},
ADDRESS = {Evanston, IL},
MONTH = {June},
KEYWORDS = {}
}
@PREAMBLE{{\def\cprime{$'$} }}
@ARTICLE{Kirichenko97,
AUTHOR = {Kirichenko, N. F.},
TITLE = {Analytical representation of perturbations of pseudo-inverse matrices},
JOURNAL = {Kibernet. Sistem. Anal.},
FJOURNAL = {Natsional\cprime naya Akademiya Nauk Ukrainy. Institut
Kibernetiki im. V. M. Glushkova. Kibernetika i Sistemny\u\i\
Analiz},
YEAR = {1997},
NUMBER = {2},
PAGES = {98--107, 189},
MRCLASS = {15A09},
MRNUMBER = {98i:15009},
NOTE = {(English translation: Cybernet. Systems Anal. 33 (1997), no. 2, 230--238)}
}
@ARTICLE{Kirkland95,
AUTHOR = {Kirkland, S. J.},
TITLE = {The group inverse associated with an irreducible periodic
nonnegative matrix},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {16},
YEAR = {1995},
NUMBER = {4},
PAGES = {1127--1134},
MRCLASS = {15A09 (15A48 15A51)},
MRNUMBER = {96i:15005}
}
@ARTICLE{KirklandNeumann94,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {Convexity and concavity of the {P}erron root and vector of {L}eslie matrices with applications to a population model},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {15},
YEAR = {1994},
NUMBER = {4},
PAGES = {1092--1107},
MRCLASS = {92D25 (15A09 15A18)},
MRNUMBER = {95e:92015}
}
@ARTICLE{KirklandNeumann95,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {Group inverses of ${M}$-matrices associated with nonnegative matrices having few eigenvalues},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {220},
YEAR = {1995},
PAGES = {181--213},
MRCLASS = {15A09 (15A18 15A48)},
MRNUMBER = {96c:15005}
}
@ARTICLE{KirklandNeumann98,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {The ${M}$-matrix group generalized inverse problem for weighted trees},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {19},
YEAR = {1998},
NUMBER = {1},
PAGES = {226--234 (electronic)},
MRCLASS = {05C50 (15A09 15A57)},
MRNUMBER = {99d:05062}
}
@ARTICLE{KirklandNeumann99,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {On group inverses of ${M}$-matrices with uniform diagonal entries},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {296},
YEAR = {1999},
NUMBER = {1-3},
PAGES = {153--170},
MRCLASS = {65Fxx (15A09)},
MRNUMBER = {1 713 277}
}
@ARTICLE{KirklandNeumann99a,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {Cutpoint decoupling and first passage times for random walks on graphs},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {20},
YEAR = {1999},
NUMBER = {4},
PAGES = {860--870 (electronic)},
MRCLASS = {60J10 (15A51 60G50)},
MRNUMBER = {2000f:60106}
}
@ARTICLE{KirklandNeumann00,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {Regular {M}arkov chains for which the transition matrix has large exponent},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {316},
YEAR = {2000},
NUMBER = {1-3},
PAGES = {45--65},
MRCLASS = {60J10},
MRNUMBER = {1 782 416}
}
@ARTICLE{KirklandNeumann00a,
AUTHOR = {Kirkland, S. J. and Neumann, M.},
TITLE = {Extremal first passage times for trees},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {48},
YEAR = {2000},
PAGES = {21--33}
}
@ARTICLE{KirklandEtAl97,
AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.},
TITLE = {Distances in weighted trees and group inverse of {L}aplacian matrices},
JOURNAL = {SIAM J. Matrix Anal. Appl.},
VOLUME = {18},
YEAR = {1997},
NUMBER = {4},
PAGES = {827--841},
MRCLASS = {15A09 (05C50)},
MRNUMBER = {98h:15005}
}
@ARTICLE{KirklandEtAl98,
AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.},
TITLE = {Bounds on the subdominant eigenvalue involving group inverses with applications to graphs},
JOURNAL = {Czechoslovak Math. J.},
VOLUME = {48(123)},
YEAR = {1998},
NUMBER = {1},
PAGES = {1--20},
MRCLASS = {15A18},
MRNUMBER = {99b:15010}
}
@ARTICLE{KirklandEtAl98a,
AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.},
TITLE = {On a bound on algebraic connectivity: the case of equality},
JOURNAL = {Czechoslovak Math. J.},
VOLUME = {48(123)},
YEAR = {1998},
NUMBER = {1},
PAGES = {65--76},
MRCLASS = {15A45 (15A51 60J10)},
MRNUMBER = {99c:15034}
}
@ARTICLE{KirklandEtAl98b,
AUTHOR = {Kirkland, S. J. and Neumann, M. and Shader, B. L.},
TITLE = {Applications of {P}az's inequality to perturbation bounds for {M}arkov chains},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {268},
YEAR = {1998},
PAGES = {183--196},
MRCLASS = {15A51 (15A12 60J10)},
MRNUMBER = {99a:15007}
}
@INCOLLECTION{Kishi64,
AUTHOR = {Kishi, F. H.},
TITLE = {On line computer control techniques and their application to re--entry aerospace vehicle control},
BOOKTITLE = {Advances in {C}ontrol {S}ystems {T}heory and
{A}pplications (C. T. Leondes, Editor)},
PAGES = {245--257},
PUBLISHER = {Academic Press},
YEAR = {1964},
ADDRESS = {New York}
}
@PREAMBLE{{\def\cprime{$'$} }}
@INCOLLECTION{Kislovskaya87,
AUTHOR = {Kislovskaya, N. M.},
TITLE = {A pseudo-inverse matrix and multiplicative groups of matrices},
BOOKTITLE = {Algorithmic and {N}umerical {P}roblems in {A}lgebra and {N}umber
{T}heory ({R}ussian)},
PAGES = {40--52, 88},
PUBLISHER = {Akad. Nauk SSSR Dal\cprime nevostochn. Otdel.},
ADDRESS = {Vladivostok},
YEAR = {1987},
MRCLASS = {15A09 (20H20)},
MRNUMBER = {90m:15008}
}
@ARTICLE{Klee62,
AUTHOR = {Klee, V.},
YEAR = {1962},
TITLE = {Review of `Linearity of Best Approximations: A Characterization of Ellipsoids' ({Rudin} and {Smith})},
JOURNAL = {Math. Reviews},
VOLUME = {23},
PAGES = {A2028},
KEYWORDS = {math, ginv, best approximation}
}
@ARTICLE{Klinger68,
AUTHOR = {Klinger, A.},
YEAR = {1968},
TITLE = {Approximate pseudoinverse solutions to ill--conditioned linear systems},
JOURNAL = {J. Optimization Th. Appl.},
VOLUME = {2},
PAGES = {117--128}
}
@TECHREPORT{KnyazevArgentati00,
AUTHOR = {Knyazev, A. V. and Argentati, M. E.},
TITLE = {An Effective and Robust Algorithm for Finding Principal Angles Between Subspaces Using An {A}-Based Scalar Product},
INSTITUTION = {Center for Computational Mathematics, University of Colorado at Denver},
YEAR = {2000},
NUMBER = {163},
MONTH = {August},
KEYWORDS = {geoa}
}
@ARTICLE{Koecher85,
AUTHOR = {Koecher, M.},
TITLE = {The generalized inverse of integral matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {71},
YEAR = {1985},
PAGES = {187--198},
MRCLASS = {15A09 (15A36)},
MRNUMBER = {87b:15007}
}
@ARTICLE{Kogbetliantz55,
AUTHOR = {Kogbetliantz, E. G.},
YEAR = {1955},
TITLE = {Solution of Linear Systems by Diagonalization of Coefficients Matrix},
JOURNAL = {Quarterly of Applied Mathematics},
VOLUME = {13},
PAGES = {123--132},
KWDS = {nla, Kogbetliantz algorithm, svd}
}
@ARTICLE{Koliha74,
AUTHOR = {Koliha, J. J.},
TITLE = {Pseudo-inverses of operators},
JOURNAL = {Bull. Amer. Math. Soc.},
VOLUME = {80},
YEAR = {1974},
PAGES = {325--328},
MRCLASS = {47A05},
MRNUMBER = {49 \#1153}
}
@ARTICLE{Koliha74a,
AUTHOR = {Koliha, J. J.},
TITLE = {Power convergence and pseudoinverses of operators in {B}anach spaces},
JOURNAL = {J. Math. Anal. Appl.},
VOLUME = {48},
YEAR = {1974},
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NUMBER = {1-4},
PAGES = {11--18},
MRCLASS = {15A09},
MRNUMBER = {94b:15001}
}
@ARTICLE{Meicler68,
AUTHOR = {Meicler, M.},
TITLE = {Chebyshev solution of an inconsistent system of $n+1$ linear equations in $n$ unknowns in terms of its least squares solution},
JOURNAL = {SIAM Rev.},
YEAR = {1968},
VOLUME = {10},
PAGES = {373--375}
}
@ARTICLE{Meicler69,
AUTHOR = {Meicler, M.},
TITLE = {A steepest ascent method for the {C}hebyshev problem},
JOURNAL = {Math. Comp.},
VOLUME = {23},
YEAR = {1969},
PAGES = {813--817},
MRCLASS = {65.30},
MRNUMBER = {41 \#2898}
}
@ARTICLE{MeisterSpeck85,
AUTHOR = {Meister, E. and Speck, F. {-O}.},
TITLE = {The {M}oore-{P}enrose inverse of {W}iener-{H}opf operators on the half axis and the quarter plane},
JOURNAL = {J. Integral Equations},
VOLUME = {9},
YEAR = {1985},
NUMBER = {1},
PAGES = {45--61},
MRCLASS = {47B35 (45E10)},
MRNUMBER = {86h:47035}
}
@PREAMBLE{{\def\cprime{$'$} }}
@ARTICLE{Meleshko76,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Statistical recurrent estimation based on pseudoinverse operators},
JOURNAL = {Avtomat. i Telemeh.},
FJOURNAL = {Avtomat. i Telemeh.},
YEAR = {1976},
NUMBER = {8},
PAGES = {101--110},
MRCLASS = {93E10},
MRNUMBER = {56 \#15050},
NOTE = {(English translation \textit{Automat. Remote Control}
\textbf{37}(1976), no. 8, part 2, 1227--1235 (1977)}
}
@ARTICLE{Meleshko77,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Pseudoinverse operators in {B}anach spaces},
JOURNAL = {Ukrain. Mat. \v Z.},
VOLUME = {29},
YEAR = {1977},
NUMBER = {6},
PAGES = {738--749, 851},
MRCLASS = {47A50},
MRNUMBER = {58 \#17910},
NOTE = {English translation: \textit{Ukrainian Math. J.}
\textbf{29} (1977), no. 6, 545--553}
}
@ARTICLE{Meleshko77a,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {A pseudo-inversion of closed operators that is stable under perturbations},
JOURNAL = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.},
VOLUME = {17},
YEAR = {1977},
NUMBER = {5},
PAGES = {1132--1143, 1332},
MRCLASS = {47A55 (65J05)},
MRNUMBER = {58 \#17922}
}
@ARTICLE{Meleshko78,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Pseudoinverse operators, and the recursive calculation of pseudosolutions in {H}ilbert spaces},
JOURNAL = {Sibirsk. Mat. \v Z.},
VOLUME = {19},
YEAR = {1978},
NUMBER = {1},
PAGES = {108--121, 238},
MRCLASS = {47A50 (65J05)},
MRNUMBER = {58 \#7148},
NOTE = {(generalization of Greville's method to Hilbert space, see
\cite{Greville60}. English translation: \textit{Siberian Math. J.}
\textbf{19} (1978), no. 1, 75--85)}
}
@ARTICLE{Meleshko79,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Perturbations of unbounded closed pseudoinverse operators},
JOURNAL = {Differentsial\cprime nye Uravneniya},
FJOURNAL = {Differentsial\cprime nye Uravneniya},
VOLUME = {15},
YEAR = {1979},
NUMBER = {4},
PAGES = {681--694, 765},
ISSN = {0374-0641},
MRCLASS = {47A50 (47A05 47A53 47A55)},
MRNUMBER = {80m:47010},
NOTE = {English translation: Differential Equations 15 (1979),
no. 4, 477--487 (1980)}
}
@ARTICLE{Meleshko79a,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {An investigation of stable ${L}$-pseudo-inverses of unbounded closed operators by the regularization method},
JOURNAL = {Differentsial\cprime nye Uravneniya},
FJOURNAL = {Differentsial\cprime nye Uravneniya},
VOLUME = {15},
YEAR = {1979},
NUMBER = {5},
PAGES = {921--935, 958--959},
MRCLASS = {47A50 (65J10)},
MRNUMBER = {80i:47020},
NOTE = {English translation: Differential Equations 15 (1979), no.
5, 653--664}
}
@ARTICLE{Meleshko79b,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Properties of pseudo-inverse operators in {B}anach spaces},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {249},
YEAR = {1979},
NUMBER = {5},
PAGES = {1055--1059},
ISSN = {0002-3264},
MRCLASS = {47A05 (47A50)},
MRNUMBER = {81a:47004},
MRREVIEWER = {C. Ilioi}
}
@ARTICLE{Meleshko80,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Filtering and identification of stochastic control systems using pseudoinverses},
JOURNAL = {Kibernetika (Kiev)},
FJOURNAL = {Otdelenie Matematiki, Mekhaniki i Kibernetiki Akademii Nauk
Ukrainsko\u \i \ SSR. Kibernetika},
YEAR = {1980},
NUMBER = {5},
PAGES = {130--140},
MRCLASS = {93E11 (93E10)},
MRNUMBER = {84k:93068}
}
@PREAMBLE{{\def\cprime{$'$} }}
@ARTICLE{Meleshko81,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Perturbed iteration methods for determining ${L}$\ generalized solutions of nonlinear operator equations},
JOURNAL = {Differentsial\cprime nye Uravneniya},
FJOURNAL = {Differentsial\cprime nye Uravneniya},
VOLUME = {17},
YEAR = {1981},
NUMBER = {3},
PAGES = {541--557, 574--575},
ISSN = {0374-0641},
MRCLASS = {47H17 (65J15)},
MRNUMBER = {82i:47097},
NOTE = {(English translation: Differential Equations 17 (1981), no. 3, 377--390)}
}
@ARTICLE{Meleshko81a,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Algorithms of pseudoinverse operators for calculating generalized solutions of nonlinear equations. {I}},
JOURNAL = {Avtomat. Sistemy Upravleniya i Pribory Avtomat.},
FJOURNAL = {Avtomatizirovannye Sistemy Upravleniya i Pribory Avtomatiki},
NUMBER = {59},
YEAR = {1981},
PAGES = {45--51, ii--iii},
MRCLASS = {65H10},
MRNUMBER = {83c:65129},
NOTE = {(Newton method, see \cite{Meleshko81b})}
}
@ARTICLE{Meleshko81b,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Algorithms of pseudoinverse operators for calculating generalized solutions of nonlinear equations. {I}{I}},
JOURNAL = {Avtomat. Sistemy Upravleniya i Pribory Avtomat.},
FJOURNAL = {Avtomatizirovannye Sistemy Upravleniya i Pribory Avtomatiki},
NUMBER = {60},
YEAR = {1981},
PAGES = {20--27},
ISSN = {0135-1710},
MRCLASS = {65H10},
MRNUMBER = {84i:65053},
NOTE = {(Newton method)}
}
@INCOLLECTION{Meleshko82,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Perturbation-resistant algorithms for pseudoinversion of rectangular matrices using the {L}agrange transform},
BOOKTITLE = {Mathematical {M}ethods of {C}ybernetics},
PAGES = {24--37},
PUBLISHER = {Akad. Nauk Ukrain. SSR Inst. Kibernet.},
ADDRESS = {Kiev},
YEAR = {1982},
MRCLASS = {65F20},
MRNUMBER = {84h:65041}
}
@PREAMBLE{{\def\cprime{$'$} }}
@ARTICLE{Meleshko85,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Regularized nonorthogonal factorizations and pseudoinversions of perturbed matrices},
JOURNAL = {Zh. Vychisl. Mat. i Mat. Fiz.},
FJOURNAL = {Akademiya Nauk SSSR. Zhurnal Vychislitel\cprime no\u\i\
Matematiki i Matematichesko\u\i\ Fiziki},
VOLUME = {26},
YEAR = {1986},
NUMBER = {4},
PAGES = {485--498, 638},
MRCLASS = {15A23 (15A09)},
MRNUMBER = {87g:15016}
}
@ARTICLE{Meleshko90,
AUTHOR = {Mele{\v{s}}ko, V. I.},
TITLE = {Accelerated regularized methods for calculating solutions of nonlinear nonregular equations},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {311},
YEAR = {1990},
NUMBER = {2},
PAGES = {282--287},
MRCLASS = {65J15 (47H17)},
MRNUMBER = {92a:65196},
NOTE = {(English translation: Soviet Math. Dokl. 41 (1990), no. 2,
246--251 (1991))}
}
@ARTICLE{MeleshkoZadachin87,
AUTHOR = {Mele{\v{s}}ko, V. I. and Zadachin, V. M.},
TITLE = {Factorizations and pseudo-inversions of singular perturbed matrices with nonfixed signs},
JOURNAL = {Izv. Vyssh. Uchebn. Zaved. Mat.},
FJOURNAL = {Izvestiya Vysshikh Uchebnykh Zavedeni\u\i. Matematika},
YEAR = {1987},
NUMBER = {11},
PAGES = {42--50, 88},
ISSN = {0021-3446},
CODEN = {IVUMBY},
MRCLASS = {15A23 (15A09 15A60 47A68)},
MRNUMBER = {89a:15013},
NOTE = {(English translation: \textit{Soviet Math.} (Iz. VUZ)
\textbf{31} (1987), no. 11, 53--62)}
}
@ARTICLE{Merz74,
AUTHOR = {Merz, G.},
TITLE = {{\"U}ber die {I}nterpolationsaufgabe bei nat\"urlichen {P}olynom-{S}plines mit {\"a}quidistanten {K}noten},
JOURNAL = {J. Approximation Theory},
VOLUME = {10},
YEAR = {1974},
PAGES = {151--158},
MRCLASS = {41A15},
MRNUMBER = {50 \#2761}
}
@ARTICLE{Metcalf65,
AUTHOR = {Metcalf, F. T.},
TITLE = {A {B}essel-{S}chwarz inequality for {G}ramians and related bounds for determinants},
JOURNAL = {Ann. Mat. Pura Appl. (4)},
VOLUME = {68},
YEAR = {1965},
PAGES = {201--232},
MRCLASS = {15.70 (15.58)},
MRNUMBER = {31 \#5874}
}
@ARTICLE{Meyer69a,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {On ranks of pseudoinverses},
JOURNAL = {SIAM Rev.},
VOLUME = {11},
YEAR = {1969},
PAGES = {382--385},
MRCLASS = {15.15},
MRNUMBER = {40 \#5630}
}
@ARTICLE{Meyer69b,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {On the construction of solutions to the matrix equations ${A}{X}={A}$ and ${Y}{A}={A}$},
JOURNAL = {SIAM Rev.},
VOLUME = {11},
YEAR = {1969},
PAGES = {612--615},
MRCLASS = {15.35},
MRNUMBER = {40 \#7284}
}
@ARTICLE{Meyer70a,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Generalized inverses of triangular matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {18},
YEAR = {1970},
PAGES = {401--406},
MRCLASS = {15.15},
MRNUMBER = {41 \#1754}
}
@ARTICLE{Meyer70b,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Some remarks on ${EP}\sb{r}$ matrices, and generalized inverses},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {3},
YEAR = {1970},
PAGES = {275--278},
MRCLASS = {15.15},
MRNUMBER = {42 \#1837}
}
@ARTICLE{Meyer70c,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Generalized inverses of block triangular matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {19},
YEAR = {1970},
PAGES = {741--750},
MRCLASS = {15.15},
MRNUMBER = {42 \#7676}
}
@ARTICLE{Meyer71,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Representations for $(1)$- and $(1,\,2)$-inverses for partitioned matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {4},
YEAR = {1971},
PAGES = {221--232},
MRCLASS = {15.15},
MRNUMBER = {43 \#7439}
}
@ARTICLE{Meyer72,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {The {M}oore-{P}enrose inverse of a bordered matrix},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {5},
YEAR = {1972},
PAGES = {375--382},
MRCLASS = {15A09},
MRNUMBER = {46 \#3522}
}
@ARTICLE{Meyer73a,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Generalized inversion of modified matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {24},
YEAR = {1973},
PAGES = {315--323},
MRCLASS = {15A09},
MRNUMBER = {47 \#5010}
}
@ARTICLE{Meyer73b,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Generalized inverses and ranks of block matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {25},
YEAR = {1973},
PAGES = {597--602},
MRCLASS = {15A09},
MRNUMBER = {48 \#8521}
}
@ARTICLE{Meyer74,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Limits and the index of a square matrix},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {26},
YEAR = {1974},
PAGES = {469--478},
MRCLASS = {15A09},
MRNUMBER = {51 \#539},
NOTE = {(see \cite{Rothblum76})}
}
@ARTICLE{Meyer75a,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {The role of the group generalized inverse in the theory of finite {M}arkov chains},
JOURNAL = {SIAM Rev.},
VOLUME = {17},
YEAR = {1975},
PAGES = {443--464},
MRCLASS = {60J10},
MRNUMBER = {52 \#4419},
KEYWORDS = {appmar, invgr}
}
@INPROCEEDINGS{Meyer82,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Analysis of finite {M}arkov chains by group inversion techniques},
CROSSREF = {Campbell82a},
PAGES = {50--81},
YEAR = {1982},
MRCLASS = {60J10 (15A09)},
MRNUMBER = {84b:60090},
KEYWORDS = {appmar, invgr}
}
@INCOLLECTION{Meyer93,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {The character of a finite {M}arkov chain},
BOOKTITLE = {Linear {A}lgebra, {M}arkov {C}hains, and {Q}ueueing
{M}odels ({M}inneapolis, {MN}, 1992)},
PAGES = {47--58},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1993},
MRCLASS = {60J10 (15A51 65F15)},
MRNUMBER = {94h:60100},
KEYWORDS = {appmar}
}
@BOOK{Meyer00,
AUTHOR = {Meyer, Jr., C. D.},
TITLE = {Matrix {A}nalysis and {A}pplied {L}inear {A}lgebra},
PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)},
ADDRESS = {Philadelphia, PA},
YEAR = {2000},
PAGES = {xii+718},
ISBN = {0-89871-454-0},
MRCLASS = {15-01},
MRNUMBER = {1 777 382}
}
@ARTICLE{MeyerPainter70,
AUTHOR = {Meyer, Jr., C. D. and Painter, R. J.},
TITLE = {Note on a least squares inverse for a matrix},
JOURNAL = {J. Assoc. Comput. Mach.},
VOLUME = {17},
YEAR = {1970},
PAGES = {110--112},
MRCLASS = {15.15},
MRNUMBER = {43 \#230}
}
@ARTICLE{MeyerPlemmons77,
AUTHOR = {Meyer, Jr., C. D. and Plemmons, R. J.},
TITLE = {Convergent powers of a matrix with applications to iterative methods for singular linear systems},
JOURNAL = {SIAM J. Numer. Anal.},
VOLUME = {14},
YEAR = {1977},
NUMBER = {4},
PAGES = {699--705},
MRCLASS = {65F20},
MRNUMBER = {56 \#4138}
}
@ARTICLE{MeyerRose77,
AUTHOR = {Meyer, Jr., C. D. and Rose, N. J.},
TITLE = {The index and the {D}razin inverse of block triangular matrices},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {33},
YEAR = {1977},
NUMBER = {1},
PAGES = {1--7},
MRCLASS = {15A09 (65F05)},
MRNUMBER = {57 \#345},
KEYWORDS = {strm, invD, indx}
}
@ARTICLE{MeyerShoaf80,
AUTHOR = {Meyer, Jr., C. D. and Shoaf, J. M.},
TITLE = {Updating finite {M}arkov chains by using techniques of group matrix inversion},
JOURNAL = {J. Statist. Comput. Simulation},
FJOURNAL = {Journal of Statistical Computation and Simulation},
VOLUME = {11},
YEAR = {1980},
NUMBER = {3-4},
PAGES = {163--181},
MRCLASS = {60J10 (15A09)},
MRNUMBER = {82d:60122}
}
@ARTICLE{MeyerStadelmaier78,
AUTHOR = {Meyer, Jr., C. D. and Stadelmaier, M. W.},
TITLE = {Singular ${M}$-matrices and inverse positivity},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {22},
YEAR = {1978},
PAGES = {139--156},
MRCLASS = {15A09},
MRNUMBER = {80b:15008}
}
@ARTICLE{MeyerStewart88,
AUTHOR = {Meyer, Jr., C. D. and Stewart, G. W.},
TITLE = {Derivatives and perturbations of eigenvectors},
JOURNAL = {SIAM J. Numer. Anal.},
VOLUME = {25},
YEAR = {1988},
NUMBER = {3},
PAGES = {679--691},
MRCLASS = {65F15 (15A22 60J10)},
MRNUMBER = {89g:65043}
}
@ARTICLE{Miao88,
AUTHOR = {Miao, Jian Ming},
TITLE = {The weighted {M}oore-{P}enrose inverse of a rank-one modified matrix (Chinese)},
JOURNAL = {J. Shanghai Teachers University},
FJOURNAL = {Journal of Shanghai Teachers University. Natural Sciences},
VOLUME = {17},
YEAR = {1988},
NUMBER = {3},
PAGES = {21--26},
MRCLASS = {15A09},
MRNUMBER = {}
}
@ARTICLE{Miao89,
AUTHOR = {Miao, Jian Ming},
TITLE = {Representations for the weighted {M}oore-{P}enrose inverse of a partitioned matrix},
JOURNAL = {J. Comput. Math.},
FJOURNAL = {Journal of Computational Mathematics. An International Journal
on Numerical Methods, Analysis and Applications},
VOLUME = {7},
YEAR = {1989},
NUMBER = {4},
PAGES = {321--323},
MRCLASS = {15A09},
MRNUMBER = {1 149 699}
}
@ARTICLE{Miao89a,
AUTHOR = {Miao, Jian Ming},
TITLE = {The {M}oore-{P}enrose inverse of a rank-$r$ modified matrix},
JOURNAL = {Numer. Math. J. Chinese Univ.},
FJOURNAL = {Numerical Mathematics. A Journal of Chinese Universities.
Gaodeng Xuexiao Jisuan Shuxue Xuebao},
VOLUME = {11},
YEAR = {1989},
NUMBER = {4},
PAGES = {355--361},
MRCLASS = {15A09},
MRNUMBER = {91a:15003}
}
@ARTICLE{Miao89b,
AUTHOR = {Miao, Jian Ming},
TITLE = {Some results on the {D}razin inverses for partitioned matrices ({C}hinese)},
JOURNAL = {J. Shanghai Teachers University},
FJOURNAL = {Journal of Shanghai Teachers University. Natural Sciences},
VOLUME = {18},
YEAR = {1989},
NUMBER = {2},
PAGES = {25--31},
MRCLASS = {15A09},
MRNUMBER = {92d:15005}
}
@ARTICLE{Miao89c,
AUTHOR = {Miao, Jian Ming},
TITLE = {Representations for the weighted {M}oore-{P}enrose inverse of sums of matrices ({C}hinese)},
JOURNAL = {Comm. Appl. Math. and Comput.},
FJOURNAL = {Communication on Applied Mathematics and Computation},
VOLUME = {3},
YEAR = {1989},
NUMBER = {2},
PAGES = {83--86},
MRCLASS = {15A09},
MRNUMBER = {1 091 143}
}
@ARTICLE{Miao90,
AUTHOR = {Miao, Jian Ming},
TITLE = {The {D}razin inverse of {H}essenberg matrices},
JOURNAL = {J. Comput. Math.},
FJOURNAL = {Journal of Computational Mathematics},
VOLUME = {8},
YEAR = {1990},
NUMBER = {1},
PAGES = {23--29},
MRCLASS = {15A09},
MRNUMBER = {}
}
@ARTICLE{Miao91,
AUTHOR = {Miao, Jian Ming},
TITLE = {General expressions for the {M}oore-{P}enrose inverse of a $2\times 2$ block matrix},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {151},
YEAR = {1991},
PAGES = {1--15},
MRCLASS = {15A09},
MRNUMBER = {92c:15005}
}
@ARTICLE{Miao93,
AUTHOR = {Miao, Jian Ming},
TITLE = {Reflexive generalized inverses and their minors},
JOURNAL = {Linear and Multilinear Algebra},
VOLUME = {35},
YEAR = {1993},
NUMBER = {2},
PAGES = {153--163},
MRCLASS = {15A09},
MRNUMBER = {95h:15007}
}
@ARTICLE{MiaoBen-Israel92,
AUTHOR = {Miao, Jian Ming and Ben-Israel, A.},
TITLE = {On principal angles between subspaces in ${R}\sp n$},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {171},
YEAR = {1992},
PAGES = {81--98},
MRCLASS = {15A45 (15A15 15A18 15A57)},
MRNUMBER = {93i:15028}
}
@ARTICLE{MiaoBen-Israel93,
AUTHOR = {Miao, Jian Ming and Ben-Israel, A.},
TITLE = {Minors of the {M}oore--{P}enrose inverse},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {195},
YEAR = {1993},
PAGES = {191--207},
MRCLASS = {15A15 (15A09 15A57)},
MRNUMBER = {95g:15007},
KEYWORDS = {det, invMP}
}
@ARTICLE{MiaoBen-Israel94,
AUTHOR = {Miao, Jian Ming and Ben-Israel, A.},
TITLE = {On $l\sb p$-approximate solutions of linear equations},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {199},
YEAR = {1994},
PAGES = {305--327},
MRCLASS = {65F20},
MRNUMBER = {95c:65065},
KEYWORDS = {aprx, norm1, normC}
}
@ARTICLE{MiaoBen-Israel95,
AUTHOR = {Miao, Jian Ming and Ben-Israel, A.},
TITLE = {The geometry of basic, approximate, and minimum-norm solutions of linear equations},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {216},
YEAR = {1995},
PAGES = {25--41},
MRCLASS = {15A06 (65F20 90C08)},
MRNUMBER = {96e:15003}
}
@ARTICLE{MiaoBen-Israel96,
AUTHOR = {Miao, Jian Ming and Ben-Israel, A.},
TITLE = {Product cosines of angles between subspaces},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {237/238},
YEAR = {1996},
PAGES = {71--81},
MRCLASS = {15A03 (15A09)},
MRNUMBER = {97d:15002}
}
@ARTICLE{MiaoRobinson88,
AUTHOR = {Miao, Jian Ming and Robinson, D. W.},
TITLE = {Group and {M}oore--{P}enrose inverses of regular morphisms with
kernel and cokernel},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {110},
YEAR = {1988},
PAGES = {263--270},
MRCLASS = {15A09 (18B99)},
MRNUMBER = {89h:15009}
}
@ARTICLE{MieheSchroder01,
AUTHOR = {Miehe, C. and Schr{\"o}der, J.},
TITLE = {Comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity},
JOURNAL = {Internat. J. Numer. Methods Engrg.},
FJOURNAL = {International Journal for Numerical Methods in Engineering},
VOLUME = {50},
YEAR = {2001},
PAGES = {273--298}
}
@ARTICLE{Mihalyffy70,
AUTHOR = {Mih{\'a}lyffy, L.},
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YEAR = {1970},
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MRCLASS = {65.35},
MRNUMBER = {42 \#5435}
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AUTHOR = {Mih{\'a}lyffy, L.},
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YEAR = {1971},
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YEAR = {1968},
PAGES = {98--113}
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AUTHOR = {Minamide, N. and Nakamura, K.},
TITLE = {Minimum error control problem in Banach space},
INSTITUTION = {Nagoya University},
YEAR = {1969},
TYPE = {Research Report of Automatic Control Lab},
NUMBER = {16},
ADDRESS = {Nagoya, Japan}
}
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AUTHOR = {Minamide, N. and Nakamura, K.},
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JOURNAL = {SIAM J. Appl. Math.},
YEAR = {1970},
VOLUME = {19},
PAGES = {167--177}
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AUTHOR = {Mitra, S. K.},
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JOURNAL = {Sankhy{\=a} Ser. A},
YEAR = {1968},
VOLUME = {30},
PAGES = {107--114}
}
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AUTHOR = {Mitra, S. K.},
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JOURNAL = {Sankhy{\=a} Ser. A},
YEAR = {1968},
VOLUME = {30},
PAGES = {323--330}
}
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AUTHOR = {Mitra, S. K.},
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JOURNAL = {Sankhy{\=a} Ser. A},
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VOLUME = {35},
PAGES = {387--392}
}
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AUTHOR = {Mitra, S. K.},
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PAGES = {213--216}
}
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AUTHOR = {Mitra, S. K.},
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YEAR = {1982},
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MRCLASS = {15A57 (15A09 15A15)},
MRNUMBER = {84g:15027}
}
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AUTHOR = {Mitra, S. K.},
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JOURNAL = {Linear Algebra and its Applications},
VOLUME = {47},
YEAR = {1982},
PAGES = {139--150},
MRCLASS = {},
MRNUMBER = {}
}
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AUTHOR = {Mitra, S. K.},
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JOURNAL = {Linear Algebra and its Applications},
VOLUME = {83},
YEAR = {1986},
PAGES = {1--27},
MRCLASS = {},
MRNUMBER = {}
}
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AUTHOR = {Mitra, S. K.},
TITLE = {On group inverses and the sharp order},
JOURNAL = {Linear Algebra and its Applications},
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YEAR = {1987},
PAGES = {17--37},
MRCLASS = {},
MRNUMBER = {}
}
@INCOLLECTION{Mitra89,
AUTHOR = {Mitra, S. K.},
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BOOKTITLE = {Statistical {D}ata {A}nalysis and {I}nference (Y. Dodge, ed.)},
PAGES = {429--443},
PUBLISHER = {North Holland},
ADDRESS = {Amsterdam},
YEAR = {1989},
MRCLASS = {},
MRNUMBER = {}
}
@ARTICLE{Mitra90,
AUTHOR = {Mitra, S. K.},
TITLE = {Shorted matrices in star and related orderings},
JOURNAL = {Circuits Systems Signal Process.},
FJOURNAL = {Circuits, Systems, and Signal Processing},
VOLUME = {9},
YEAR = {1990},
NUMBER = {2},
PAGES = {197--212},
MRCLASS = {94C05 (15A99 47A63)},
MRNUMBER = {91m:94039}
}
@ARTICLE{Mitra91,
AUTHOR = {Mitra, S. K.},
TITLE = {Matrix partial order through generalized inverses: unified theory},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {148},
YEAR = {1991},
PAGES = {237--263},
MRCLASS = {15A09},
MRNUMBER = {92e:15011}
}
@ARTICLE{Mitra94,
AUTHOR = {Mitra, S. K.},
TITLE = {Separation theorems},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {208/209},
YEAR = {1994},
PAGES = {239--256},
MRCLASS = {15A09 (15A24 15A99)},
MRNUMBER = {95e:15004}
}
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AUTHOR = {Mitra, S. K.},
TITLE = {Erratum: ``{T}he nonunique shorted matrix'' [{L}inear {A}lgebra {A}ppl.\ {\bf 237/238} (1996), 41--70; {M}{R} 97a:15012] by {M}itra and {K}. {M}. {P}rasad},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {260},
YEAR = {1997},
PAGES = {323},
MRCLASS = {15A09 (15A45 47A63)},
MRNUMBER = {1 448 364}
}
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AUTHOR = {Mitra, S. K.},
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YEAR = {1999},
NUMBER = {1-3},
PAGES = {271--288},
MRCLASS = {15A09},
MRNUMBER = {2000b:15002}
}
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AUTHOR = {Mitra, S. K. and Bhimasankaram, P.},
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JOURNAL = {Sankhy\=a Ser. A},
VOLUME = {33},
YEAR = {1971},
PAGES = {395--410},
MRCLASS = {62J05 (15A09)},
MRNUMBER = {47 \#2760}
}
@ARTICLE{MitraHartwig92,
AUTHOR = {Mitra, S. K. and Hartwig, R. E.},
TITLE = {Partial orders based on outer inverses},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {176},
YEAR = {1992},
PAGES = {3--20},
MRCLASS = {15A09 (15A06 15A24)},
MRNUMBER = {93m:15008}
}
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AUTHOR = {Mitra, S. K. and Odell, P. L.},
TITLE = {On parallel summability of matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {74},
YEAR = {1986},
PAGES = {239--255},
MRCLASS = {15A48},
MRNUMBER = {87d:15014}
}
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AUTHOR = {Mitra, S. K. and Prasad, K. M.},
TITLE = {The nonunique shorted matrix},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {237/238},
YEAR = {1996},
PAGES = {41--70},
MRCLASS = {15A09 (15A45 47A63)},
MRNUMBER = {97a:15012},
NOTE = {(erratum in \cite{Mitra97})}
}
@ARTICLE{MitraPrasad97a,
AUTHOR = {Mitra, S. K. and Prasad, K. M.},
TITLE = {The nonunique parallel sum},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {259},
YEAR = {1997},
PAGES = {77--99},
MRCLASS = {15A30 (15A09 47A63)},
MRNUMBER = {98g:15023}
}
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AUTHOR = {Mitra, S. K. and Puri, M. L.},
TITLE = {Shorted operators and generalized inverses of matrices},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {25},
YEAR = {1979},
PAGES = {45--56},
MRCLASS = {15A09},
MRNUMBER = {80b:15009}
}
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AUTHOR = {Mitra, S. K. and Puri, M. L.},
TITLE = {Shorted matrices---an extended concept and some applications},
JOURNAL = {Linear Algebra and its Applications},
VOLUME = {42},
YEAR = {1982},
PAGES = {57--79},
MRCLASS = {15A04 (15A24 94C05)},
MRNUMBER = {83e:15003}
}
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VOLUME = {14},
YEAR = {1983},
NUMBER = {4},
PAGES = {241--258},
MRCLASS = {15A09 (15A99)},
MRNUMBER = {84f:15009}
}
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AUTHOR = {Mitra, S. K. and Rao, C. R.},
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YEAR = {1968},
VOLUME = {30},
PAGES = {281--290}
}
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YEAR = {1974},
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MRCLASS = {15A60},
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VOLUME = {58},
YEAR = {1984},
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MRCLASS = {},
MRNUMBER = {}
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BOOKTITLE = {Questions on {N}umerical {M}athematics},
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PUBLISHER = {Akad. Nauk Ukrain. SSR Inst. Kibernet.},
ADDRESS = {Kiev},
YEAR = {1980},
MRCLASS = {65N99 (65F20)},
MRNUMBER = {82m:65111}
}
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AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.},
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YEAR = {1982},
NUMBER = {3},
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MRCLASS = {65N05},
MRNUMBER = {83e:65160},
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AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.},
TITLE = {A weighted pseudoinverse for complex matrices},
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YEAR = {1983},
NUMBER = {1},
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MRCLASS = {15A09 (65F20)},
MRNUMBER = {84e:15004}
}
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AUTHOR = {Mol{\v{c}}anov, I. N. and Galba, {\=E}. F.},
TITLE = {Weighted pseudo-inversion of matrices with positive-definite weights},
JOURNAL = {Dokl. Akad. Nauk Ukrain. SSR Ser. A},
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Fiziko-Matematicheskie i Tekhnicheskie Nauki},
YEAR = {1989},
NUMBER = {7},
PAGES = {15--17, 85},
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MRNUMBER = {90j:15011}
}
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AUTHOR = {Moler, C. B.},
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PAGES = {316--321}
}
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AUTHOR = {Moler, C. B. and Van Loan, C. F.},
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VOLUME = {20},
YEAR = {1978},
NUMBER = {},
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MRCLASS = {},
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AUTHOR = {M{\"o}nch, W.},
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JOURNAL = {Z. Angew. Math. Mech.},
VOLUME = {58},
YEAR = {1978},
NUMBER = {2},
PAGES = {67--74},
MRCLASS = {65F20},
MRNUMBER = {57 \#18056}
}
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AUTHOR = {M{\"o}nch, W.},
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YEAR = {1982},
NUMBER = {1},
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ISSN = {0010-485X},
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MRNUMBER = {83a:65001}
}
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AUTHOR = {Mond, B.},
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PAGES = {393--399}
}
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AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.},
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JOURNAL = {Bull. Austral. Math. Soc.},
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}
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AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.},
TITLE = {Inequalities with weights for powers of generalized inverses. {I}{I}},
JOURNAL = {Linear Algebra and its Applications},
FJOURNAL = {Linear Algebra and its Applications},
VOLUME = {210},
YEAR = {1994},
PAGES = {265--272},
MRCLASS = {15A45 (15A09 15A48)},
MRNUMBER = {95h:15031}
}
@ARTICLE{MondPecaric96,
AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.},
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VOLUME = {19},
YEAR = {1996},
NUMBER = {4},
PAGES = {707--710},
MRCLASS = {15A09 (15A45)},
MRNUMBER = {97d:15007},
KEYWORDS = {matpsd, ineq, invMP}
}
@ARTICLE{MondPecaric98,
AUTHOR = {Mond, B. and Pe{\v{c}}ari{\'c}, J. E.},
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YEAR = {1998},
NUMBER = {4},
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MRCLASS = {15A09},
MRNUMBER = {99k:15006}
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AUTHOR = {Moore, E. H.},
TITLE = {On a form of general analysis with applications to linear differential equations and integral equations},
BOOKTITLE = {Atti del IV Congresso Internazionale dei Matematici (Rome 1908). Vol 2},
PAGES = {98--114},
PUBLISHER = {},
ADDRESS = {Roma},
YEAR = {1909},
MRCLASS = {},
MRNUMBER = {}
}
@INCOLLECTION{Moore10,
AUTHOR = {Moore, E. H.},
TITLE = {Introduction to a {F}orm of {G}eneral {A}nalysis},
BOOKTITLE = {The New Haven Mathematical Colloquium},
PAGES = {1--150},
PUBLISHER = {Yale University Press},
ADDRESS = {New Haven, CT},
YEAR = {1910},
NOTE = {(see review in \cite{Birkhoff11})}
}
@ARTICLE{Moore12,
AUTHOR = {Moore, E. H.},
YEAR = {1912},
TITLE = {On the foundations of the theory of linear integral equations},
JOURNAL = {Trans. Amer. Math. Soc.},
VOLUME = {18},
PAGES = {334-362},
KEYWORDS = {History, Moore, integral equations}
}
@INCOLLECTION{Moore12a,
AUTHOR = {Moore, E. H.},
TITLE = {On the fundamental functional operation of a general theory of linear integral equations},
BOOKTITLE = {Proceedings of the 5th {I}nternational {C}ongress of {M}athematicians},
PAGES = {230--255},
PUBLISHER = {},
ADDRESS = {Cambridge},
YEAR = {1912}
}
@ARTICLE{Moore15,
AUTHOR = {Moore, E. H.},
YEAR = {1915},
TITLE = {Definition of limit in general integral analysis},
JOURNAL = {Proc. Nat. Acad. Sci.},
VOLUME = {1},
PAGES = {628}
}
@ARTICLE{Moore16,
AUTHOR = {Moore, E. H.},
YEAR = {1916},
TITLE = {On properly positive {H}ermitian matrices},
JOURNAL = {Bull. Amer. Math. Soc.},
VOLUME = {23},
PAGES = {59},
KEYWORDS = {reproducing kernels}
}
@ARTICLE{Moore20,
AUTHOR = {Moore, E. H.},
YEAR = {1920},
TITLE = {On the Reciprocal of the General Algebraic Matrix},
JOURNAL = {Bull. Amer. Math. Soc.},
VOLUME = {26},
PAGES = {394-395},
NOTE = {(Abstract)},
KEYWORDS = {History, Moore-Penrose inverse, determinantal representation}
}
@BOOK{Moore35,
AUTHOR = {Moore, E. H. and Barnard, R. W.},
YEAR = {1935},
TITLE = {General {A}nalysis},
SERIES = {Memoirs of the American Philosophical Society, I},
PUBLISHER = {American Philosophical Society},
ADDRESS = {Philadelphia, Pennsylvania},
NOTE = {(see specially Part 1, pp. 197--209)},
KEYWORDS = {book, alglin, his, ginv}
}
@ARTICLE{MooreSmith22,
AUTHOR = {Moore, E. H. and Smith, H. L.},
YEAR = {1922},
TITLE = {A general theory of limits},
JOURNAL = {Amer. J. Math.},
VOLUME = {44},
PAGES = {102--121}
}
@INCOLLECTION{MooreNashed73,
AUTHOR = {Moore, R. H. and Nashed, M. Z.},
TITLE = {Approximations of generalized inverses of linear operators in {B}anach spaces},
BOOKTITLE = {Approximation {T}heory ({P}roc. {I}nternat. {S}ympos., {U}niv. {T}exas,
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PAGES = {425--428},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1973},
MRCLASS = {47A55},
MRNUMBER = {48 \#9429}
}
@ARTICLE{MooreNashed74,
AUTHOR = {Moore, R. H. and Nashed, M. Z.},
TITLE = {Approximations to generalized inverses of linear operators},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {27},
YEAR = {1974},
PAGES = {1--16},
MRCLASS = {47A55 (65J05)},
MRNUMBER = {50 \#14301},
KEYWORDS = {invMP, pert, spacB, linop}
}
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AUTHOR = {Moppert, C. F.},
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JOURNAL = {Quart. J. Math. Oxford Ser. (2)},
VOLUME = {10},
YEAR = {1959},
PAGES = {161--164},
MRCLASS = {46.00 (15.00)},
MRNUMBER = {22 \#176}
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AUTHOR = {Morley, T. D.},
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VOLUME = {70},
YEAR = {1979},
NUMBER = {1},
PAGES = {33--41},
MRCLASS = {94C05 (47B15)},
MRNUMBER = {80g:94075},
KEYWORDS = {apphys, appnet, matpsd, proj, parsum}
}
@ARTICLE{Morley79b,
AUTHOR = {Morley, T. D.},
TITLE = {A {G}auss-{M}arkov theorem for infinite-dimensional regression models with possibly singular covariance},
JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {37},
YEAR = {1979},
NUMBER = {2},
PAGES = {257--260},
MRCLASS = {62J05},
KEYWORDS = {GauMar, spacH, inv1},
MRNUMBER = {80m:62069}
}
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AUTHOR = {Morley, T. D.},
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YEAR = {1990},
TITLE = {On Bounds For Scaled Projections and Pseudo-Inverses},
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NOTE = {(Answer to a question in \cite{Stewart89})}
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AUTHOR = {Pereyra, V. and Rosen, J. B.},
TITLE = {Computation of the pseudoinverse of a matrix of unknown rank},
INSTITUTION = {Dept. of Computer Science, Stanford University},
YEAR = {1964},
MONTH = {Sept.},
NUMBER = {CS 13},
ADDRESS = {Stanford, CA},
KEYWORDS = {},
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AUTHOR = {Peters, G. and Wilkinson, J. H.},
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MRCLASS = {92A25 (41A15 68T05 92A09)},
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AUTHOR = {Pokorn{\'a}, Olga},
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MRCLASS = {65F20},
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YEAR = {1990}
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AUTHOR = {Poole, G. D. and Barker, G. P.},
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YEAR = {1979},
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MRNUMBER = {80e:15004}
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AUTHOR = {Poole, G. D. and Boullion, T. L.},
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JOURNAL = {SIAM J. Appl. Math.},
VOLUME = {23},
YEAR = {1972},
PAGES = {171--172},
MRCLASS = {15A09},
MRNUMBER = {47 \#5011}
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VOLUME = {22},
YEAR = {1972},
PAGES = {35--37},
MRCLASS = {15A09},
MRNUMBER = {46 \#9059}
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AUTHOR = {Poole, G. D. and Boullion, T. L.},
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PAGES = {94--103},
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ADDRESS = {Berlin},
YEAR = {1980},
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AUTHOR = {Pye, W. C. and Boullion, T. L. and Atchison, T. A.},
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YEAR = {1967},
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MRCLASS = {65.10 (15.00)},
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JOURNAL = {SIAM J. Appl. Math.},
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YEAR = {1972},
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MRCLASS = {90C05 (15A09)},
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AUTHOR = {Pyle, L. D. and Cline, R. E.},
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JOURNAL = {SIAM. J. Appl. Math.},
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@PREAMBLE{{\def\cprime{$'$} }}
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AUTHOR = {Pyt{\cprime}ev, Yu. P.},
TITLE = {A pseudoinverse operator. {P}roperties and applications},
JOURNAL = {Mat. Sb. (N.S.)},
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ADDRESS = {London}
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@TECHREPORT{Rabson69,
AUTHOR = {Rabson, G.},
TITLE = {The generalized inverse in set theory and matrix theory},
INSTITUTION = {Dept. of Mathematics, Clarkson College of Technology},
YEAR = {1969},
ADDRESS = {Potsdam, NY}
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AUTHOR = {Radi{\'c}, M.},
TITLE = {A definition of the determinant of a rectangular matrix},
JOURNAL = {Glasnik Mat. Ser. III},
VOLUME = {1 (21)},
YEAR = {1966},
PAGES = {17--22},
MRCLASS = {15.20},
MRNUMBER = {35 \#201},
KEYWORDS = {detgen}
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AUTHOR = {Radi{\'c}, M.},
TITLE = {On a generalization of the {A}rghiriade-{D}ragomir representation of the {M}oore-{P}enrose inverse},
JOURNAL = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)},
VOLUME = {44},
YEAR = {1968},
PAGES = {333--336},
MRCLASS = {15.15},
MRNUMBER = {38 \#4495},
KEYWORDS = {invMP, mateq, sollsq}
}
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AUTHOR = {Rado, R.},
TITLE = {Note on generalized inverses of matrices},
JOURNAL = {Proceedings of the Cambridge Philosophical Society},
YEAR = {1956},
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PAGES = {600--601}
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AUTHOR = {Rahman, M. Abdur},
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AUTHOR = {Rako{\v{c}}evi{\'c}, V.},
TITLE = {Moore--{P}enrose inverse in {B}anach algebras},
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MRCLASS = {46H05 (47A05)},
MRNUMBER = {90a:46118}
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AUTHOR = {Rako{\v{c}}evi{\'c}, V.},
TITLE = {On the continuity of the {M}oore-{P}enrose inverse in {B}anach algebras},
JOURNAL = {Facta Univ. Ser. Math. Inform.},
FJOURNAL = {Facta Universitatis. Series: Mathematics and Informatics},
NUMBER = {6},
YEAR = {1991},
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MRCLASS = {46H05 (47A05)},
MRNUMBER = {94c:46098}
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AUTHOR = {Rako{\v{c}}evi{\'c}, V.},
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AUTHOR = {Rako{\v{c}}evi{\'c}, V. and Wei, Yimin},
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AUTHOR = {Rakowski, M.},
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AUTHOR = {Rall, L. B.},
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AUTHOR = {Ralston, A. and Rabinowitz, P.},
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AUTHOR = {Ramamurthy, K. G. and Mohan, S. R.},
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AUTHOR = {Randall, J. H. and Rayner, A. A.},
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