On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems
In the present paper, we are concerned by weighted Arnoldi like methods for solving large and sparse linear systems that have different right-hand sides but have the same coefficient matrix. We first give detailed descriptions of the weighted Gram-Schmidt process and of a Ruhe variant of the weighte...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2018-07-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32109 |
| _version_ | 1797633536320077824 |
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| author | Lakhdar Elbouyahyaoui Mohammed Heyouni |
| author_facet | Lakhdar Elbouyahyaoui Mohammed Heyouni |
| author_sort | Lakhdar Elbouyahyaoui |
| collection | DOAJ |
| description | In the present paper, we are concerned by weighted Arnoldi like methods for solving large and sparse linear systems that have different right-hand sides but have the same coefficient matrix. We first give detailed descriptions of the weighted Gram-Schmidt process and of a Ruhe variant of the weighted block Arnoldi algorithm. We also establish some theoretical results that links the iterates of the weighted block Arnoldi process to those of the non weighted one. Then, to accelerate the convergence of the classical restarted block and seed GMRES methods, we introduce the weighted restarted block and seed GMRES methods. Numerical experiments that are done with different matrices coming from the Matrix Market repository or from the university of Florida sparse matrix collection are reported at the end of this work in order to compare the performance and show the effectiveness of the proposed methods. |
| first_indexed | 2024-03-11T11:55:21Z |
| format | Article |
| id | doaj.art-ed08ea55ca94422796c4ab957f7e5f6f |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:21Z |
| publishDate | 2018-07-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-ed08ea55ca94422796c4ab957f7e5f6f2023-11-08T20:10:09ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-07-0136310.5269/bspm.v36i3.3210915679On applying weighted seed techniques to GMRES algorithm for solving multiple linear systemsLakhdar Elbouyahyaoui0Mohammed Heyouni1Centre des métiers de l’éducation et de la formation-CRMEFUniversité Mohammed PremierIn the present paper, we are concerned by weighted Arnoldi like methods for solving large and sparse linear systems that have different right-hand sides but have the same coefficient matrix. We first give detailed descriptions of the weighted Gram-Schmidt process and of a Ruhe variant of the weighted block Arnoldi algorithm. We also establish some theoretical results that links the iterates of the weighted block Arnoldi process to those of the non weighted one. Then, to accelerate the convergence of the classical restarted block and seed GMRES methods, we introduce the weighted restarted block and seed GMRES methods. Numerical experiments that are done with different matrices coming from the Matrix Market repository or from the university of Florida sparse matrix collection are reported at the end of this work in order to compare the performance and show the effectiveness of the proposed methods.https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32109Block Krylov subspace methodsblock Arnoldi processblock GMRESseed GMRES |
| spellingShingle | Lakhdar Elbouyahyaoui Mohammed Heyouni On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems Boletim da Sociedade Paranaense de Matemática Block Krylov subspace methods block Arnoldi process block GMRES seed GMRES |
| title | On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems |
| title_full | On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems |
| title_fullStr | On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems |
| title_full_unstemmed | On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems |
| title_short | On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems |
| title_sort | on applying weighted seed techniques to gmres algorithm for solving multiple linear systems |
| topic | Block Krylov subspace methods block Arnoldi process block GMRES seed GMRES |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32109 |
| work_keys_str_mv | AT lakhdarelbouyahyaoui onapplyingweightedseedtechniquestogmresalgorithmforsolvingmultiplelinearsystems AT mohammedheyouni onapplyingweightedseedtechniquestogmresalgorithmforsolvingmultiplelinearsystems |