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020 _a9783034806060
_9978-3-0348-0606-0
024 7 _a10.1007/978-3-0348-0606-0
_2doi
035 _ato000541795
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA184-205
072 7 _aPBF
_2bicssc
072 7 _aMAT002050
_2bisacsh
082 0 4 _a512.5
_223
100 1 _aEidelman, Yuli.
_eauthor.
_9333923
245 1 0 _aSeparable Type Representations of Matrices and Fast Algorithms
_helectronic resource
_bVolume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms /
_cby Yuli Eidelman, Israel Gohberg, Iulian Haimovici.
260 _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
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 0 _amathematics.
_9566183
650 0 _aMatrix theory.
_9303236
650 0 _aNumerical analysis.
_9566288
650 1 4 _aMathematics.
_9566184
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
_9303237
650 2 4 _aNumerical Analysis.
_9566289
700 1 _aGohberg, Israel.
_eauthor.
_9331543
700 1 _aHaimovici, Iulian.
_eauthor.
_9447740
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aOperator Theory: Advances and Applications,
_9566535
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0606-0
912 _aZDB-2-SMA
999 _c399763