Some observations on weighted GMRES

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Guettel, Stefan and Pestana, Jennifer (2014) Some observations on weighted GMRES. Numerical Algorithms, 67 (4). pp. 733-752. ISSN 1017-1398 (https://doi.org/10.1007/s11075-013-9820-x)

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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.

ORCID iDs

Guettel, Stefan and Pestana, Jennifer ORCID logoORCID: https://orcid.org/0000-0003-1527-3178;
  • Item type:Article
    ID code:54749
    Dates:
    Date
    Event
    December 2014
    Published
    10 January 2014
    Published Online
    13 December 2013
    Accepted
    Notes:The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-013-9820-x
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Dec 2015 01:26
    Last modified:11 Nov 2024 11:14
    URI:https://strathprints.strath.ac.uk/id/eprint/54749
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