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Functions of Matrices: Theory and Computation

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by Nicholas J. Higham


2008 / xx + 425 pages / Hardcover / ISBN 978-0-898716-46-7 / List Price $70.00 / SIAM Member Price $49.00 / Order Code OT104

Keywords: numerical analysis, numerical linear algebra, matrix analysis, matrix function, matrix computations

Table of Contents
Sample Chapter

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"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

Matrix functions are of growing interest due to their fascinating theory and the many applications in which they provide insight and succinct solutions. Functions of Matrices: Theory and Computation gives a thorough treatment of the theory of matrix functions and numerical methods for computing them, as well as an overview of applications.

The book is useful for advanced courses and is well-suited to self-study. The broad content—including f(A)-related facts, tricks, and techniques, historical references, and an appendix of background results—makes it convenient as a general reference in matrix analysis and numerical linear algebra.

Key features of the book:

  • Elegant treatment of the theory of matrix functions, exploiting the equivalent definitions of f(A) via the Jordan form, polynomial interpolation, and the Cauchy integral formula.
  • Develops theory of conditioning and properties of the FrŽchet derivative.
  • Emphasizes Schur decomposition, block Parlett recurrence, and judicious use of PadŽ approximants.
  • General results on convergence and stability of matrix iterations.
  • Detailed treatment of the matrix sign function, matrix roots, the polar decomposition, and transcendental matrix functions (exponential, logarithm, cosine, sine).
  • Thorough analysis of the accuracy, stability, and computational cost of numerical methods.
  • A chapter devoted to the f(A)b problem.
  • Extensive collection of problems with solutions.
  • Matrix Function Toolbox provides MATLAB™ implementations of key algorithms.

This book is for specialists in numerical analysis and applied linear algebra as well as anyone wishing to learn about the theory of matrix functions and state of the art methods for computing them. It can be used for a graduate-level course on functions of matrices and is a suitable reference for an advanced course on applied or numerical linear algebra. It is also particularly well suited for self-study.

About the Author
Nicholas J. Higham, FRS, is Richardson Professor of Applied Mathematics at The University of Manchester, UK. He is the author of more than 100 publications and of the books Accuracy and Stability of Numerical Algorithms (SIAM, 2nd ed., 2002), Handbook of Writing for the Mathematical Sciences, (SIAM, 2nd ed., 1998), and MATLAB Guide, (with Desmond J. Higham, SIAM, 2nd ed., 2005).

ISBN: 9780898716467

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