| Restarted FOM Augmented with Ritz Vectors for Shifted Linear Systems |
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| 作者姓名： | Zhanwen Li Guiding Gu |
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| 作者单位： | Zhanwen Li and Guiding Gu 1 Department of Mathematics，Hebei University of Science and Technology，Shijiazhuang 050018，China.2 Department of Applied Mathematics，Shanghai University of Finance and Economics，Shanghai 200433，China. |
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| 摘 要： | The restarted FOM method presented by Simoncini7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method.
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| 关 键 词： | Krylov空间 FOM 重新启动 移动线性系统 质量因数 |
| 收稿时间： | 2003-07-18 |
| 修稿时间： | 2004-05-30 |
Restarted FOM Augmented with Ritz Vectors for Shifted Linear Systems |
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| Zhanwen Li Guiding Gu.Restarted FOM Augmented with Ritz Vectors for Shifted Linear Systems[J].Numerical Mathematics A Journal of Chinese Universities English Series,2006,15(1):40-49. |
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| Authors: | Zhanwen Li Guiding Gu |
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| Abstract: | The restarted FOM method presented by Simoncini7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method. |
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| Keywords: | Augmented Krylov subspace FOM restarting shifted systems |
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