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2013.83: Some observations on weighted GMRES

2013.83: Stefan Güttel and Jen Pestana (2013) Some observations on weighted GMRES.

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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 a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These 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:MIMS Preprint
Additional Information:

Accepted for publication in Numerical Algorithms

Uncontrolled Keywords:weighted GMRES, linear systems, Krylov subspace method, harmonic Ritz values
Subjects:MSC 2000 > 65 Numerical analysis
MIMS number:2013.83
Deposited By:Stefan Güttel
Deposited On:13 December 2013

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