| 预处理后新分裂下的SOR迭代法收敛性讨论 |
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| 引用本文： | 王慧勤,雷刚. 预处理后新分裂下的SOR迭代法收敛性讨论[J]. 安徽大学学报(自然科学版), 2010, 34(4) |
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| 作者姓名： | 王慧勤 雷刚 |
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| 作者单位： | 宝鸡文理学院,数学系,陕西,宝鸡,721013 |
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| 基金项目： | 国家自然科学基金资助项目,宝鸡文理学院科研基金资助项目 |
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| 摘 要： | 在求解大型线性方程组Ax=b时,常采用预处理方法求解,也就是对方程组两边同时乘以非奇异矩阵P再求解.运用矩阵分裂理论及比较定理,给出一种预处理后改进的SOR迭代方法,与现有的方法进行比较,证明这种方法不仅能加速SOR迭代法的收敛性,而且优于一般的预处理方法.最后给出一个数值例子.
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| 关 键 词： | 预处理 收敛性 SOR迭代法 谱半径 |
The convergence discussion of the SOR iterative method in preconditioned for the new splitting |
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| WANG Hui-qin,LEI Gang. The convergence discussion of the SOR iterative method in preconditioned for the new splitting[J]. Journal of Anhui University(Natural Sciences), 2010, 34(4) |
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| Authors: | WANG Hui-qin LEI Gang |
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| Affiliation: | WANG Hui-qin,LEI Gang(Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013,China) |
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| Abstract: | When solving the large linear systems Ax=b,the preconditioned method was used generally,it was let nonsingular matrix P to mount the linear systems.This paper by using matrix iterative analysis and comparison theorems,made an improved SOR iterative method in preconditioned,then proved the improved method not only to accelerate the SOR iterative method,but also to excelled the general preconditioned SOR method.Last the numerical example was given. |
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| Keywords: | precondition convergence the SOR iteration method spectral radius |
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