Implementation of a Restarted Krylov Subspace Method for the Evaluation of Matrix Functions

Abstract

A new implementation of restarted Krylov subspace methods for evaluating f(A)b for a function f , a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp(A)b.

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Cite this paper

@inproceedings{Afanasjew2005ImplementationOA, title={Implementation of a Restarted Krylov Subspace Method for the Evaluation of Matrix Functions}, author={Martin Afanasjew and Michael Eiermann and Oliver G. Ernst and Stefan G{\"{u}ttel and Richard S. Varga}, year={2005} }