| 求解大型稀疏线性方程组的不完全SAOR预条件共轭梯度法 |
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| 引用本文： | 温瑞萍,孟国艳,王川龙.求解大型稀疏线性方程组的不完全SAOR预条件共轭梯度法[J].工程数学学报,2007,24(4):712-718. |
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| 作者姓名： | 温瑞萍 孟国艳 王川龙 |
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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系,忻州,034000 |
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| 基金项目： | 山西省自然科学基金项目青年学术带头人经费(20011041) |
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| 摘 要： | 预条件共轭梯度法是求解大型稀疏线性方程组的有效方法之一,SSOR预条件方法是基于矩阵分裂的较有效的预条件共轭梯度法。通过矩阵分裂,本文讨论不完全SAOR预条件方法,研究此方法的预条件因子及系数矩阵的预条件数,并证明了此方法的预条件数小于SSOR预条件方法的预条件数。最后通过求解离散化波松(Poisson)方程组表明了该方法的有效性。
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| 关 键 词： | 不完全SAOR 预条件共轭梯度法 条件数 |
| 文章编号： | 1005-3085（2007）04-0712-07 |
| 修稿时间： | 2005-12-30 |
Incomplete SAOR Preconditioning Algorithms for Solving Large Sparse Linear Systems |
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| WEN Rui-ping,MENG Guo-yan,WANG Chuan-long.Incomplete SAOR Preconditioning Algorithms for Solving Large Sparse Linear Systems[J].Chinese Journal of Engineering Mathematics,2007,24(4):712-718. |
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| Authors: | WEN Rui-ping MENG Guo-yan WANG Chuan-long |
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| Abstract: | The preconditioned conjugate gradient method is one of efficient methods for solving large sparse linear equations. In this paper, we proposed an incomplete SAOR preconditioned method by matrix splitting. We studied the preconditioned factor and the preconditioned number. Furthermore, it is proved that the preconditioned number is smaller than the SSOR preconditioned number. Finally, the proposed algorithm's effect is illustrated by solving discrete Poisson equations. |
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| Keywords: | incomplete SAOR preconditioned conjugate gradient method condition number |
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