Some observations on weighted GMRES

Stefan Guettel, Jennifer Pestana

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)733-752
Number of pages21
JournalNumerical Algorithms
Volume67
Issue number4
Early online date10 Jan 2014
DOIs
Publication statusPublished - Dec 2014

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GMRES
Linear systems
Computational complexity
Weighting
GMRES Method
Arnoldi
Krylov Subspace Methods
Preconditioner
Computational Complexity
Linear Systems
Observation
Alternatives

Keywords

  • weighted GMRES
  • linear systems
  • Krylov subspace method
  • harmonic Ritz values
  • algorithms
  • algebra

Cite this

Guettel, Stefan ; Pestana, Jennifer. / Some observations on weighted GMRES. In: Numerical Algorithms. 2014 ; Vol. 67, No. 4. pp. 733-752.
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Some observations on weighted GMRES. / Guettel, Stefan; Pestana, Jennifer.

In: Numerical Algorithms, Vol. 67, No. 4, 12.2014, p. 733-752.

Research output: Contribution to journalArticle

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