A pattern-based restarted GMRES

John M. Dennis

Elizabeth R. Jessup

Department of Computer Science
University of Colorado at Boulder
Boulder, Colorado 80309


The traditional wisdom concerning GMRES(m) is that the larger the restart size 'm', the closer GMRES(m) mimics the convergence behavior of standard GMRES. It has been shown, however, that a smaller restart size can actually benefit certain small test problems. A modification called GMRES(P) replaces a single fixed restart size 'm' with a restart pattern 'P' where the restart size varies after each restart. GMRES(P) allows for the examination of this paradoxical behavior on a more general set of matrices. We observe that decreasing the Krylov subspace size for select restarts can reduce iteration counts. This talk will cover ongoing work on this phenomenon.