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Functions of Matrices: Theory and Computation
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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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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“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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Metadata
- 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
- 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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