| 非对称线性方程组的二阶段分裂迭代法 |
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| 引用本文： | 温瑞萍,孟国艳,关晋瑞.非对称线性方程组的二阶段分裂迭代法[J].计算数学,2012,34(4):405-412. |
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| 作者姓名： | 温瑞萍 孟国艳 关晋瑞 |
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| 作者单位： | 1. 太原师范学院数学系, 太原 030012;
2. 忻州师范学院计算机科学系, 山西忻州 034000 |
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| 基金项目： | 国家自然科学基金项目(11071184);山西省自然科学基金项目(2010011006, 2012011015-6);山西回国留学人员基金项目(2010087);山西省高等学校科技开发项目(20101112) |
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| 摘 要： | 本文针对非对称正定矩阵提出了一个收敛分裂, 给出了分裂收敛的充要条件. 在此基础上, 提出系数为非对称正定矩阵的线性方程组的二阶段算法, 并讨论了算法的收敛条件. 最后, 通过数值例子展示了算法的有效性.
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| 关 键 词： | 非对称正定矩阵 二阶段 收敛性 线性方程组 |
| 收稿时间： | 2012-05-24; |
TWO-STAGE ITERATIVE METHOD FOR NON-SYMMETRIC LINEAR SYSTEMS |
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| Wen Ruiping,Meng Guoyan,Guan Jinrui.TWO-STAGE ITERATIVE METHOD FOR NON-SYMMETRIC LINEAR SYSTEMS[J].Mathematica Numerica Sinica,2012,34(4):405-412. |
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| Authors: | Wen Ruiping Meng Guoyan Guan Jinrui |
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| Institution: | 1. Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, China;
2. Department of computer Science, Xinzhou Normal University, Xinzhou 034000, Shanxi, China |
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| Abstract: | In this paper, we come up with a convergent splitting for non-symmetric positive definite matrix, derive sufficient and necessary conditions to guarantee that the splitting is convergent. We present two-stage algorithm for solving a non-symmetric positive definite linear systems, and discuss the convergent condition of new algorithm. Finally, numerical examples show that the algorithm can significantly improve the convergence of the iterative method. |
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| Keywords: | non-symmetric positive definite matrix two-stage convergence linear systems |
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