On the influence of the orthogonalization scheme on the parallel performance of GMRES

TitreOn the influence of the orthogonalization scheme on the parallel performance of GMRES
Publication TypeConference Paper
Year of Publication1998
AuthorsFraysse, V, Giraud, L, Kharraz-Aroussi, H
EditorPritchard, D, Reeve, J
Conference NameEURO-PAR `98 PARALLEL PROCESSING
PublisherUniv Southampton, Dept Electron & Comp Sci, Concurrent Computat Grp
ISBN Number3-540-64952-2
Abstract

In Krylov-based iterative methods, the computation of an orthonormal basis of the Krylov space is a key issue in the algorithms because the many scalar products are often a bottleneck in parallel distributed environments. Using GMRES, we present a comparison of four variants of the Gram-Schmidt process on distributed memory machines. Our experiments are carried on an application in astrophysics and on a convection-diffusion example. We show that the iterative classical Gram-Schmidt method overcomes its three competitors in speed and in parallel scalability while keeping robust numerical properties.

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