2010.18: Computing Matrix Functions
2010.18: Nicholas J. Higham and Awad H. AlMohy (2010) Computing Matrix Functions. Acta Numerica, 19. 159 208. ISSN 09624929
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DOI: 10.1017/S0962492910000036
Abstract
The need to evaluate a function $f(A)\in\mathbb{C}^{n \times n}$ of a matrix $A\in\mathbb{C}^{n \times n}$ arises in a wide and growing number of applications, ranging from the numerical solution of differential equations to measures of the complexity of networks. We give a survey of numerical methods for evaluating matrix functions, along with a brief treatment of the underlying theory and a description of two recent applications. The survey is organized by classes of methods, which are broadly those based on similarity transformations, those employing approximation by polynomial or rational functions, and matrix iterations. Computation of the Fr\'echet derivative, which is important for condition number estimation, is also treated, along with the problem of computing $f(A)b$ without computing $f(A)$. A summary of available software completes the survey.
Item Type:  Article 

Additional Information: 

Uncontrolled Keywords:  matrix $p$th root, primary matrix function, nonprimary matrix function, Markov chain, transition matrix, matrix exponential, SchurParlett method, CICADA 
Subjects:  MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis 
MIMS number:  2010.18 
Deposited By:  Nick Higham 
Deposited On:  18 May 2010 
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