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Functions of matrices : theory and computation / Nicholas J. Higham

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Other titles in applied mathematics ; 104Publisher: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2008Description: Online-Ressource (1 electronic text xx, 425 p.)ISBN:
  • 9780898716467
  • 0898716462
  • 9780898717778
  • 9780898717778
Subject(s): Additional physical formats: 0898716462 | Erscheint auch als Druck-AusgabeDDC classification:
  • 512.9/434 22
MSC: MSC: *15-01 | 15-XX | 65FxxRVK: RVK: SK 220 | SK 780 | SK 905LOC classification:
  • QA188
DOI: DOI: 10.1137/1.9780898717778Online resources: Additional physical formats: Also available in print version.
Contents:
Includes bibliographical references (p. 379-413) and index
1. Theory of matrix functions -- 2. Applications -- 3. Conditioning -- 4. Techniques for general functions -- 5. Matrix sign function -- 6. Matrix square root -- 7. Matrix pth root -- 8. The polar decomposition -- 9. Schur-Parlett algorithm -- 10. Matrix exponential -- 11. Matrix logarithm -- 12. Matrix cosine and sine -- 13. Function of matrix times vector : f (A)b -- 14. Miscellany.
f (A)b -- 14. Miscellany
Summary: Includes bibliographical references (p. 379-413) and indexSummary: A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithmsPPN: PPN: 680115633Package identifier: Produktsigel: ZDB-72-SIA
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