| 关于正定可对称化线性代数方程组的预对称正则化算法 |
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| 引用本文： | 李维国,陈金海.关于正定可对称化线性代数方程组的预对称正则化算法[J].高等学校计算数学学报,2006,28(2):151-161. |
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| 作者姓名： | 李维国 陈金海 |
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| 作者单位： | 石油大学数学与计算科学学院,东营,257061 |
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| 摘 要： | 1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法12,16,17]．但非对称的系数
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| 关 键 词： | 线性代数方程组 正则化算法 对称化 正定 非奇异 R^n |
| 收稿时间： | 03 2 2004 12:00AM |
| 修稿时间： | 2004-03-02 |
PRE-SYMMETRY REGULARIZED METHOD FOR POSITIVE DEFINITE SYMMETRIZABLE SYSTEM OF LINEAR ALGEBRAIC EQUATIONS |
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| Li Weiguo,Chen Jinhai.PRE-SYMMETRY REGULARIZED METHOD FOR POSITIVE DEFINITE SYMMETRIZABLE SYSTEM OF LINEAR ALGEBRAIC EQUATIONS[J].Numerical Mathematics A Journal of Chinese Universities,2006,28(2):151-161. |
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| Authors: | Li Weiguo Chen Jinhai |
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| Abstract: | In this paper,we present a kind of pre-symmetry regularized method for the nonsymmetric linear equations system.Based on combination pre- symmetric technique and regularized conjugated gradient method,the new algorithm-pre-symmetry regularized conjugated gradient (PRCG) method,is pre- sented.Theoretical analysis and numerical computations show behaviors of the new method are more efficient and robust than LRSCG method presented in pa- per1]and those of Krylov methods,which are usual adopted for solving general nonsymmmetric systems,such as GMRES,CGS etc. |
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| Keywords: | positive definite symmetrizable matrix conjugate gradient method regularized ill-condition linear system |
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