Some observations on weighted GMRES
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...
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| Format: | Report |
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Unspecified
2012
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| _version_ | 1826306157227016192 |
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| author | Guettel, S Pestana, J |
| author_facet | Guettel, S Pestana, J |
| author_sort | Guettel, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T06:43:40Z |
| format | Report |
| id | oxford-uuid:fa264d58-a42d-47a1-99b4-44ed1d10ba6a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:43:40Z |
| publishDate | 2012 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:fa264d58-a42d-47a1-99b4-44ed1d10ba6a2022-03-27T13:03:28ZSome observations on weighted GMRESReporthttp://purl.org/coar/resource_type/c_93fcuuid:fa264d58-a42d-47a1-99b4-44ed1d10ba6aMathematical Institute - ePrintsUnspecified2012Guettel, SPestana, JWe 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. |
| spellingShingle | Guettel, S Pestana, J Some observations on weighted GMRES |
| title | Some observations on weighted GMRES |
| title_full | Some observations on weighted GMRES |
| title_fullStr | Some observations on weighted GMRES |
| title_full_unstemmed | Some observations on weighted GMRES |
| title_short | Some observations on weighted GMRES |
| title_sort | some observations on weighted gmres |
| work_keys_str_mv | AT guettels someobservationsonweightedgmres AT pestanaj someobservationsonweightedgmres |