Computing $f(A)b$ for Matrix Functions $f$

Davies, Philip I. and Higham, Nicholas J. (2005) Computing $f(A)b$ for Matrix Functions $f$. In: QCD and Numerical Analysis III. Lecture Notes in Computational Science and Engineering, 47 . Springer-Verlag, Berlin, pp. 15-24. ISBN 3-540-21257-4

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Abstract

For matrix functions $f$ we investigate how to compute a matrix-vector product $f(A)b$ without explicitly computing $f(A)$. A general method is described that applies quadrature to the matrix version of the Cauchy integral theorem. Methods specific to the logarithm, based on quadrature, and fractional matrix powers, based on solution of an ordinary differential equation initial value problem, are also presented

Item Type:	Book Section
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Nick Higham
Date Deposited:	01 Dec 2005
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/96

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