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

Functions of Matrices: Theory and Computation

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

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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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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Crossref · 10.1137/1.9780898717778

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  • The Kronecker product can transform the linear matrix equation AX + XB = C into the vectorized form D vec[X] = vec[C], where D is a square matrix depending on A and B.

    “With the help of the Kronecker product, a problem like (49) may be solved by factoring out X in the form of a column vector from the l.h.s. turning the equation into (see for example [35, 36])”

    From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [36]

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Authors
Higham, N. J.
Affiliations
University of Manchester (GB)
Corresponding author
Higham, Nicholas J.
Venue
Society for Industrial and Applied Mathematics eBooks
Published
2008-01-01
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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