QCD and Numerical Analysis III

Volume 47 of the series Lecture Notes in Computational Science and Engineering pp 15-24

Computing f(A)b for Matrix Functions f

  • Philip I. DaviesAffiliated withSchool of Mathematics, University of Manchester
  • , Nicholas J. HighamAffiliated withSchool of Mathematics, University of Manchester

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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