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 07:41 
Last Modified:  29 May 2015 19:17 
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