A simple strategy for varying the restart parameter in GMRES(m)

Authors:
A. H. Baker;E. R. Jessup;Tz. V. Kolev
Affiliations:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Box 808 L-560, Livermore, CA 94551, United States;Department of Computer Science, University of Colorado, Boulder, CO 80309-0430, United States;Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Box 808 L-560, Livermore, CA 94551, United States
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.