QCD and Numerical Analysis III pp 15-24
Computing f(A)b for Matrix Functions f
- 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
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
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