A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-C...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/457089 |
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| author | Ke Zhang Chuanqing Gu |
| author_facet | Ke Zhang Chuanqing Gu |
| author_sort | Ke Zhang |
| collection | DOAJ |
| description | The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-d2b594b381724fa2b1237983d0c653fb |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d2b594b381724fa2b1237983d0c653fb2025-02-03T06:44:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/457089457089A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand SidesKe Zhang0Chuanqing Gu1Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaThe restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2013/457089 |
| spellingShingle | Ke Zhang Chuanqing Gu A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides Journal of Applied Mathematics |
| title | A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides |
| title_full | A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides |
| title_fullStr | A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides |
| title_full_unstemmed | A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides |
| title_short | A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides |
| title_sort | polynomial preconditioned global cmrh method for linear systems with multiple right hand sides |
| url | http://dx.doi.org/10.1155/2013/457089 |
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