Some observations on weighted GMRES

Stefan Güttel, Jennifer Pestana

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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. © 2014 Springer Science+Business Media New York.
Original languageEnglish (US)
Pages (from-to)733-752
Number of pages20
JournalNumerical Algorithms
Volume67
Issue number4
DOIs
StatePublished - Jan 10 2014
Externally publishedYes

Fingerprint

Dive into the research topics of 'Some observations on weighted GMRES'. Together they form a unique fingerprint.

Cite this