LEADER 05178nam 22006375 450 001 9910300142003321 005 20220330172116.0 010 $a3-0348-0606-X 024 7 $a10.1007/978-3-0348-0606-0 035 $a(CKB)3710000000025631 035 $a(EBL)1538776 035 $a(SSID)ssj0001049622 035 $a(PQKBManifestationID)11575127 035 $a(PQKBTitleCode)TC0001049622 035 $a(PQKBWorkID)11020011 035 $a(PQKB)10188007 035 $a(MiAaPQ)EBC1538776 035 $a(DE-He213)978-3-0348-0606-0 035 $a(PPN)176102906 035 $a(EXLCZ)993710000000025631 100 $a20131008d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSeparable type representations of matrices and fast algorithms $evolume 1 basics. completion problems. multiplication and inversion algorithms /$fby Yuli Eidelman, Israel Gohberg, Iulian Haimovici 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (404 p.) 225 1 $aOperator Theory: Advances and Applications,$x0255-0156 ;$v234 300 $aDescription based upon print version of record. 311 $a3-0348-0605-1 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike. 410 0$aOperator Theory: Advances and Applications,$x0255-0156 ;$v234 606 $aMatrix theory 606 $aAlgebra 606 $aNumerical analysis 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aNumerical analysis. 615 14$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aNumerical Analysis. 676 $a512.9434 676 $a512.9434 700 $aEidelman$b Yuli$4aut$4http://id.loc.gov/vocabulary/relators/aut$0315664 702 $aGohberg$b Israel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aHaimovici$b Iulian$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300142003321 996 $aSeparable Type Representations of Matrices and Fast Algorithms$92504760 997 $aUNINA