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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 $evolume 2 eigenvalue method /$fby Yuli Eidelman, Israel Gohberg, Iulian Haimovici
205   $a1st ed. 2014.
210  1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014.
215   $a1 online resource (358 p.)
225 1 $aOperator Theory: Advances and Applications,$x0255-0156 ;$v235
300   $aDescription based upon print version of record.
311   $a3-0348-0611-6 
327   $aPart 5. The eigenvalue structure of order one quasiseparable matrices -- 21. Quasiseparable of order one matrices. Characteristic polynomials -- 22. Eigenvalues with geometric multiplicity one -- 23. Kernels of quasiseparable of order one matrices -- 24. Multiple eigenvalues -- Part 6. Divide and conquer method for eigenproblems -- 25. Divide step -- 26. Conquer step and rational matrix functions eigenproblem -- 27. Complete algorithm for Hermitian matrices -- 28. Complete algorithm for unitary Hessenberg matrices -- Part 7. Algorithms for qr iterations and for reduction to Hessenberg form -- 29. The QR iteration method for eigenvalues -- 30. The reduction to Hessenberg form -- 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices -- Part 8. QR iterations for companion matrices -- 32. Companion and unitary matrices -- 33. Explicit methods -- 34. Implicit methods with compression -- 35. The factorization based implicit method -- 36. Implicit algorithms based on the QR representation -- Bibliography.  .
330   $aThis two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
410  0$aOperator Theory: Advances and Applications,$x0255-0156 ;$v235
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
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   $a9910300143303321
996   $aSeparable Type Representations of Matrices and Fast Algorithms$92504760
997   $aUNINA