Computing f(A)b for Matrix Functions f

  • Philip I. Davies
  • Nicholas J. Higham
Conference paper

DOI: 10.1007/3-540-28504-0_2

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

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Philip I. Davies
    • 1
  • Nicholas J. Higham
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterEngland

Personalised recommendations