Automated parameter selection for rational Arnoldi approximation of Markov functions

Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present a heuristic for the automated pole selection when the function to be approximated is of Markov type, such as the matrix square root. The performance of this approach is demonstrated at several numerical examples. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)