Functions of Matrices: Theory and Computation

by Nicholas J. Higham

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theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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

450 pages, Hardcover

First published March 26, 2008

About the author

Librarian note: There are other authors with the same name.

Nicholas John Higham FRS is a numerical analyst and Richardson Professor of Applied Mathematics at the School of Mathematics, University of Manchester.

He is a graduate of the Victoria University of Manchester gaining his BA in 1982, MSc in and 1983 and PhD 1985. His PhD thesis was entitled Nearness Problems in Numerical Linear Algebra and his supervisor was George Hall. Higham is Director of Research within the School of Mathematics, Director of the Manchester Institute for Mathematical Sciences (MIMS), and Head of the Numerical Analysis Group. He held a prestigious Royal Society Wolfson Research Merit Award (2003–2008) and as of 2006[update] is on the Institute for Scientific Information Highly Cited Researcher list.