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005 20140103192748.0
008 131008s2014 sz | s ||0| 0|eng d
020 $a9783034806060
020 $a9783034806060
020 $a9783034806053
024 7 $a10.1007/978-3-0348-0606-0$2doi
035 $a(Springer)9783034806060
040 $aSpringer
050 4 $aQA184-205
072 7 $aPBF$2bicssc
072 7 $aMAT002050$2bisacsh
082 04 $a512.5$223
100 1 $aEidelman, Yuli,$eauthor.
245 10 $aSeparable Type Representations of Matrices and Fast Algorithms :$bVolume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms /$cby Yuli Eidelman, Israel Gohberg, Iulian Haimovici.
264 1 $aBasel :$bSpringer Basel :$bImprint: Birkhäuser,$c2014.
300 $aXV, 399 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aOperator Theory: Advances and Applications,$x0255-0156 ;$v234
505 0 $aPart 1. Basics on separable, semiseparable and quasiseparable representations of matrices -- 1. Matrices with separable representation and low complexity algorithms -- 2. The minimal rank completion problem -- 3. Matrices in diagonal plus semiseparable form -- 4. Quasiseparable representations: the basics -- 5. Quasiseparable generators -- 6. Rank numbers of pairs of mutually inverse matrices, Asplund theorems -- 7. Unitary matrices with quasiseparable representations -- Part 2. Completion of matrices with specified bands -- 8. Completion to Green matrices -- 9. Completion to matrices with band inverses and with minimal ranks -- 10. Completion of special types of matrices -- 11. Completion of mutually inverse matrices -- 12. Completion to unitary matrices -- Part 3. Quasiseparable representations of matrices, descriptor systems with boundary conditions and first applications -- 13. Quasiseparable representations and descriptor systems with boundary conditions -- 14. The first inversion algorithms -- 15. Inversion of matrices in diagonal plus semiseparable form -- 16. Quasiseparable/semiseparable representations and one-direction systems -- 17. Multiplication of matrices -- Part 4. Factorization and inversion -- 18. The LDU factorization and inversion -- 19. Scalar matrices with quasiseparable order one -- 20. The QR factorization based method.
520 $aThis two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
650 20 $aNumerical analysis.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aMatrix theory.
650 0 $aNumerical analysis.
650 24 $aLinear and Multilinear Algebras, Matrix Theory.
700 1 $aHaimovici, Iulian,$eauthor.
700 1 $aGohberg, I.$q(Israel),$d1928-2009,$eauthor.
776 08 $iPrinted edition:$z9783034806053
830 0 $aOperator theory, advances and applications ;$v234.
988 $a20131221
906 $0VEN