Separable type representations of matrices and fast algorithms : Volume 2 Eigenvalue Method /
This 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 algo...
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| 格式: | 电子书 |
| 语言: | English |
| 出版: |
Basel
Springer Basel
2014.
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| 丛编: | Operator Theory: Advances and Applications
235 |
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| 在线阅读: | Click here to view the full text content |
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书本目录:
- 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. .