Separable Type Representations of Matrices and Fast Algorithms Volume 2 Eigenvalue Method /

• Κύριοι συγγραφείς: Eidelman, Yuli (Συγγραφέας), Gohberg, Israel (Συγγραφέας), Haimovici, Iulian (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
• Σειρά: Operator Theory: Advances and Applications, 235
• Θέματα: Mathematics.; Matrix theory.; Algebra.; Numerical analysis.; Linear and Multilinear Algebras, Matrix Theory.; Numerical Analysis.

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...

Πίνακας περιεχομένων:

• 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.  .