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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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 Frechet 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 algorithms.
Rezensionen / Stimmen
This superb book is timely and is written with great attention paid to detail, particularly in its referencing of the literature. The book has a wonderful blend of theory and code (MATLAB (R)) so will be useful both to nonexperts and to experts in the field.""- Alan Laub, Professor, University of California, Los Angeles
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 265 mm
Breite: 188 mm
Dicke: 30 mm
Gewicht
ISBN-13
978-0-89871-646-7 (9780898716467)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Nicholas J. Higham, FRS, is Richardson Professor of Applied Mathematics at the University of Manchester, UK.
List of Figures
List of Tables
Preface
Chapter 1: Theory of Matrix Functions
Chapter 2: Applications
Chapter 3: Conditioning
Chapter 4: Techniques for General Functions
Chapter 5: Matrix Sign Function
Chapter 6: Matrix Square Root
Chapter 7: Matrix pth Root
Chapter 8: The Polar Decomposition
Chapter 9: Schur-Parlett Algorithm
Chapter 10: Matrix Exponential
Chapter 11: Matrix Logarithm
Chapter 12: Matrix Cosine and Sine
Chapter 13: Function of Matrix Times Vector: f(A)b
Chapter 14: Miscellany
Appendix A: Notation
Appendix B: Background: Definitions and Useful Facts
Appendix C: Operation Counts
Appendix D: Matrix Function Toolbox
Appendix E: Solutions to Problems
Bibliography
Index.
