解线性方程组的预条件AOR迭代法分析  

Analysis of Preconditioned AOR Iterative Methods in Solving Linear Systems

作　　者：赵秋霞[1] 

机构地区：[1]运城学院应用数学系

出　　处：《课程教育研究》2016年第33期194-194,共1页Course education research

摘　　要：自然科学的诸多领域的许多问题最终都转化为大型线性方程组的求解,而这些方程组的求解一般采用迭代法。对迭代法而言,当迭代矩阵的谱半径小于1时,谱半径越小其收敛速度越快,有效降低迭代矩阵谱半径的方法就是对线性方程组本身进行预处理。因此预条件方法成为一个热点问题。本文对几个预条件AOR迭代法进行程序实现,并对结果进行分析。The solutions of many problems in the field of natural scienee are eventually turned into the solutions of large linear systems. Generally, the linear systems are solved by iterative methods. The smaller it is, the faster the method converges for iterative method when the spectral radius of the iterative matrix is smaller than 1. The effective method to decrease the spectral radius of iterative matrices is to precondition linear systems. Therefore, the study of the preconditioned methods is a hot topic. In this thesis, some preconditioned AOR iterative methods are implemented by computer programs and the results are compared with basic iterative methods.

关 键 词：线性方程组 迭代解法 预条件方法 AOR 方法 谱半径 

分 类 号：G642[文化科学—高等教育学]