The Mathematical Institute, University of Oxford, Eprints Archive

Some observations on weighted GMRES

Güttel, S. and Pestana, J. (2012) Some observations on weighted GMRES. Numerical Algorithms . (Submitted)

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Abstract

We investigate the convergence of the weighted GMRES method
for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present new alternative implementations of the weighted Arnoldi algorithm which may be favorable in terms of computational complexity, and examine stability issues connected with these implementations. Two implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1591
Deposited By:Peter Hudston
Deposited On:01 Sep 2012 08:41
Last Modified:01 Sep 2012 08:41

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