| CGS/GMRES(k): AN ADAPTIVE PRECONDITIONED CGS ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS |
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| 作者姓名： | 曹海燕 李兴伟 |
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| 作者单位： | Cao Hai-yan Li Xing-wei Institute of Mathematics，Fudan University，Shanghai 200433，PRC. |
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| 基金项目： | Supported by the State Major Key Project for Basic Researches，the Doctorial Program Foundation of China |
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| 摘 要： | Recently Y. Saad proposed a flexible inner-outer preconditioned GMRES algorithm for nonsymmetric linear systems 4]. Following their ideas, we suggest an adaptive preconditioned CGS method, called CGS/GMRES (k), in which the preconditioner is constructed in the iteration step of CGS, by several steps of GMRES(k). Numerical experiments show that the residual of the outer iteration decreases rapidly. We also found the interesting residual behaviour of GMRES for the skewsymmetric linear system Ax = b, which gives a convergence result for restarted GMRES (k). For convenience, we discuss real systems.
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CGS/GMRES(k): AN ADAPTIVE PRECONDITIONED CGS ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS* |
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| Cao Hai-yan Li Xing-wei Institute of Mathematics,Fudan University,Shanghai ,PRC..CGS/GMRES(k): AN ADAPTIVE PRECONDITIONED CGS ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS[J].Numerical Mathematics A Journal of Chinese Universities English Series,1998(2). |
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| Authors: | Cao Hai-yan Li Xing-wei Institute of Mathematics Fudan University Shanghai PRC |
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| Institution: | Cao Hai-yan Li Xing-wei Institute of Mathematics,Fudan University,Shanghai 200433,PRC. |
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| Abstract: | Recently Y. Saad proposed a flexible inner-outer preconditioned GMRES algorithm for nonsymmetric linear systems 4]. Following their ideas, we suggest an adaptive preconditioned CGS method, called CGS/GMRES(k), in which the preconditioner is constructed in the iteration step of CGS, by several steps of GMRES(k). Numerical experiments show that the residual of the outer iteration decreases rapidly. We also found the interesting residual behaviour of GMRES for the skewsymmetric linear system Ax - b, which gives a convergence result for restarted GMRES (k). For convenience, we discuss real systems. |
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| Keywords: | Krylov subspace methods CGS GMRES |
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