SOR迭代法收敛的充要条件  

The sufficient and necessary conditions of the convergence of the SOR iterative method

作　　者：许国[1] 

机构地区：[1]山东建筑工程学院数理系,山东济南250014

出　　处：《山东建筑工程学院学报》2002年第4期93-95,共3页Journal of Shandong Institute of Architecture and Engineering

摘　　要：超松弛迭代法(简称SOR法)是解决大型稀疏矩阵方程组的有效方法之一,是一种一阶线性定常迭代法。从介绍解线性代数方程组的SOR方法入手,通过对矩阵的谱半径的讨论,推出且证明了一个判定SOR迭代法收敛的充分且必要条件,并递推出SOR迭代法发散的判定条件,申明了选取松弛因子对迭代法的收敛速度的影响及准确选取松弛因子的重要性。The successive over-relaxation method (SOR method) is one of the effective methods to solve large sparse matrix eguation sets. It is a kind of one-order linear constant iterative method. By introduc-ing SOR method of solving linear equation sets and discussing spectrum radius of matrix, this paper de-duces and proves a sufficient and necessary condition judging the convergence of the SOR method. A judging condition of the divergence of the SOR method is also deduced, The influence of choosing loose factor to the convergence speed and the importance of choosing accurate loose factors are explaining.

关 键 词：充要条件 SOR迭代法 谱半径 松弛因子 

分 类 号：O241[理学—计算数学]