| 重新启动的FOM方法求解多右端位移方程组 |
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| 引用本文： | 李占稳,汪勇,顾桂定.重新启动的FOM方法求解多右端位移方程组[J].上海大学学报(英文版),2005,9(2):107-113. |
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| 作者姓名： | 李占稳 汪勇 顾桂定 |
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| 作者单位： | [1]DepartmentofMathematics,CollegeofSciences,ShanghaiUniversity,Shanghai200444,P.R.China [2]DepartmentofAppliedMathematics,ShanghaiUniversityofFinanceandEconomics,Shanghai200433,P.R.China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Grant No.10271075) |
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| 摘 要： | The seed method is used for solving multiple linear systems A^(i) x^(i) = b^(i) for l≤ i≤ s , where the coefficient matrix A^(i) and the right-hand side b^(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A^(i) . In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is repeated until all the systems are solved.
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| 关 键 词： | 线性系统 转移系统 FOM 子空间 种子方法 矩阵 |
| 收稿时间： | 11 November 2003 |
Researted FOM for multiple shifted linear systems |
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| Li?Zhan-wen,Wang?Yong,Gu?Gui-ding.Researted FOM for multiple shifted linear systems[J].Journal of Shanghai University(English Edition),2005,9(2):107-113. |
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| Authors: | Li Zhan-wen Wang Yong Gu Gui-ding |
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| Institution: | 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P.R.China
2. Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, P.R. China |
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| Abstract: | The seed method is used for solving multiple linear systems A
(i)
x
(i)=b(i) for 1⩽i≤s, where the coefficient matrix A
(i) and the right-hand side b
(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A
(i). In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices.
One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are
projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is
repeated until all the systems are solved.
Project supported by the National Natural Science Foundation of China (Grant No. 10271075) |
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| Keywords: | multiple linear systems seed method Krylov subspace FOM shifted systems |
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