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Separable type representations of matrices and fast algorithms : volume 1 basics. completion problems. multiplication and inversion algorithms / / by Yuli Eidelman, Israel Gohberg, Iulian Haimovici
| Separable type representations of matrices and fast algorithms : volume 1 basics. completion problems. multiplication and inversion algorithms / / by Yuli Eidelman, Israel Gohberg, Iulian Haimovici |
| Autore | Eidelman Yuli |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2014 |
| Descrizione fisica | 1 online resource (404 p.) |
| Disciplina | 512.9434 |
| Collana | Operator Theory: Advances and Applications |
| Soggetto topico |
Matrix theory
Algebra Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis |
| ISBN | 3-0348-0606-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part 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. |
| Record Nr. | UNINA-9910300142003321 |
Eidelman Yuli
|
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| Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Separable type representations of matrices and fast algorithms : volume 2 eigenvalue method / / by Yuli Eidelman, Israel Gohberg, Iulian Haimovici
| Separable type representations of matrices and fast algorithms : volume 2 eigenvalue method / / by Yuli Eidelman, Israel Gohberg, Iulian Haimovici |
| Autore | Eidelman Yuli |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2014 |
| Descrizione fisica | 1 online resource (358 p.) |
| Disciplina | 512.9434 |
| Collana | Operator Theory: Advances and Applications |
| Soggetto topico |
Matrix theory
Algebra Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis |
| ISBN | 3-0348-0612-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part 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. . |
| Record Nr. | UNINA-9910300143303321 |
|
Eidelman Yuli
|
||
| Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||