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QCD and Numerical Analysis III pp 15–24Cite as

Computing f(A)b for Matrix Functions f

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 47))

Summary

For matrix function 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

This work was supported by Engineering and Physical Sciences Research Council grant GR/R22612.

Supported by a Royal Society-Wolfson Research Merit Award.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, England

    Philip I. Davies & Nicholas J. Higham

Authors
  1. Philip I. Davies
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  2. Nicholas J. Higham
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Editor information

Editors and Affiliations

  1. School of Physics, University of Edinburgh, Mayfield Road, EH9 3JZ, Edinburgh, UK

    Artan Bori~i , Bálint Joó , Anthony Kennedy  & Brian Pendleton , ,  & 

  2. Fachbereich C — Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42097, Wuppertal, Germany

    Andreas Frommer

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Davies, P.I., Higham, N.J. (2005). Computing f(A)b for Matrix Functions f. In: Bori~i, A., Frommer, A., Joó, B., Kennedy, A., Pendleton, B. (eds) QCD and Numerical Analysis III. Lecture Notes in Computational Science and Engineering, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28504-0_2

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