| 预条件后新分裂下的Gauss-Seidel迭代法收敛性讨论 |
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| 引用本文： | 雷刚.预条件后新分裂下的Gauss-Seidel迭代法收敛性讨论[J].科学技术与工程,2010,10(27). |
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| 作者姓名： | 雷刚 |
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| 作者单位： | 宝鸡文理学院数学系,宝鸡,721013 |
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| 基金项目： | 宝鸡文理学院重点项目基金 |
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| 摘 要： | 针对Gauss-Seidel迭代法求解大型线性方程组Ax=b时,结合矩阵分裂理论及比较定理,给方程两边同时左乘非奇异矩阵P(也称为预条件矩阵),对新的系数矩阵PA进行矩阵分裂时,引入参数α,以使矩阵分裂更加一般化,说明这种方法不仅能加速Gauss-Seidel迭代法的收敛,而且优于一般的预条件方法.最后给出一个数值例子.
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| 关 键 词： | 预条件 收敛性 Gauss-Seidel迭代法 谱半径 |
| 收稿时间： | 6/24/2010 3:22:43 PM |
| 修稿时间： | 6/24/2010 3:22:43 PM |
The convergence discussion of the Gauss-Seidel iterative method in the new matrix splitting |
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| Lei-Gang.The convergence discussion of the Gauss-Seidel iterative method in the new matrix splitting[J].Science Technology and Engineering,2010,10(27). |
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| Authors: | Lei-Gang |
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| Institution: | LEI Gang(Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013,P.R.China) |
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| Abstract: | This paper discuss the Gauss-Seidel iterative method to solve the large linear system by using matrix iterative analysis and comparison theorems, make the nonsingular matrix ( preconditioned matrix )to left multiply the linear system two-sided. This article pull in the parameter to splitting the new coefficient matix, then prove the improved method not only to accelerate the Gauss-Seidel iterative method, but also to excel the general preconditioned method. Last the numerical example is given. |
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| Keywords: | precondition convergence the SOR iteration method spectral radius |
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