Cited by 2,113Matrix Theory and AlgorithmsNumerical Methods and AlgorithmsMathematical and Computational Methods

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Functions of Matrices: Theory and Computation

Higham, Nicholas J.·2008·Society for Industrial and Applied Mathematics eBooks

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Abstract

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theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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

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Authors: Higham, N. J.
Affiliations: University of Manchester (GB)
Corresponding author: Higham, Nicholas J.
ORCID: Higham, Nicholas J.
Venue: Society for Industrial and Applied Mathematics eBooks
Publisher: Society for Industrial and Applied Mathematics
Published: 2008-01-01
DOI: 10.1137/1.9780898717778
OpenAlex: W1483804921
Cited by: 2,113
References: 0
Citations by year: 2026: 133 · 2025: 114 · 2024: 124 · 2023: 115 · 2022: 121 · 2021: 171 · 2020: 177 · 2019: 152 · 2018: 140 · 2017: 125 · 2016: 132 · 2015: 126 · 2014: 120 · 2013: 100 · 2012: 76
FWCI: 19.22
Type: book
Language: en
Open access: closed
Locations: Society for Industrial and Applied Mathematics eBooks (publishedVersion)
Topics: Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
Keywords: matrix functions, matrix sign function, matrix roots, conditioning, Fréchet derivative, Schur decomposition, numerical stability, computational cost, matrix iteration, convergence, stability, MATLAB algorithm

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