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Functions of Matrices

Theory and Computation

Nicholas J. Higham (author)

ISBN: 9780898716467

Publication Date: Mar 2008

Format: Hardback

The only book devoted exclusively to matrix functions, this research monograph gives a thorough treatment of the theory of matrix functions and numerical methods for computing them. Its wide-ranging content makes it useful as a general reference in numerical linear algebra.

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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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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 Fréchet 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.


"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®) so will be useful both to nonexperts and to experts in the field."- Alan Laub, Professor, University of California, Los Angeles
Pages 445
Dimensions 229 x 152
Date Published 30 Mar 2008
Publisher SIAM - Society for Industrial and Applied Mathematics
Subject/s Applied mathematics   Numerical analysis  
  • 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.
Nicholas J. Higham, FRS, is Richardson Professor of Applied Mathematics at the University of Manchester, UK.

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