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基于矩阵分裂的预处理(I+S)后SOR迭代法收敛性分析
引用本文:雷刚.基于矩阵分裂的预处理(I+S)后SOR迭代法收敛性分析[J].贵州大学学报(自然科学版),2011,28(4):6-10.
作者姓名:雷刚
作者单位:宝鸡文理学院数学系,陕西宝鸡,721013
基金项目:国家自然科学基金资助项目(10071048); 宝鸡文理学院重点项目基金资助(zk1031)
摘    要:在运用SOR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(也称为预处理矩阵),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,说明这种方法能加速SOR迭代法的收敛性,而且比一般的预处理方法更有效.最后给出数值例子加以说明.

关 键 词:预条件  收敛性  SOR迭代法  谱半径  矩阵分裂

The Convergence Analysis of the SOR Iterative Method in Preconditioned(I+S) on the Based Matrix Splitting
LEI Gang.The Convergence Analysis of the SOR Iterative Method in Preconditioned(I+S) on the Based Matrix Splitting[J].Journal of Guizhou University(Natural Science),2011,28(4):6-10.
Authors:LEI Gang
Institution:LEI Gang (Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013,China)
Abstract:The SOR iterative method was introduced to solve the large linear system Ax=b by using matrix iterative analysis and comparison theorems,make the nonsingular matrix P(preconditioned matrix) to left multiply the linear system two-sided.This paper adjoins in the parameter α to splitting the new coefficient matrix,then prove the improved method not only to accelerate the SOR iterative method,but also to excel the general preconditioned method.At last the numerical example is given.
Keywords:precondition  convergence  the SOR iteration method  spectral radius  matrix splitting  
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