解线性方程组的预条件Gauss-Seidel型迭代法  

Preconditioned Gauss-Seidel Type Iterative Methods for Solving Linear Systems

作　　者：程光辉[1] 黄廷祝[1] 成孝予[1] 

机构地区：[1]电子科技大学应用数学学院,成都610054

出　　处：《应用数学和力学》2006年第9期1117-1121,共5页Applied Mathematics and Mechanics

基　　金：教育部"新世纪人才支持计划"基金资助项目(2004);四川省应用基础研究基金资助项目(05JY029-068-2)

摘　　要：给出了解线性方程组的预条件Gauss-Seidel型方法,提出了选取合适的预条件因子.并讨论了对Z-矩阵应用这种方法的收敛性,给出了收敛最快时的系数取值.最后给出数值例子,说明选取合适的预条件因子应用Gauss-Seidel方法求解线性方程组是有效的.The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, was presented. Convergence of the preconditioned method applied to Z-matrices was discussed. Also the optimal parmeter was presented. Numerical results show that the proper choice of the preconditioner can lead to effective the preconditioned Gauss-Seidel type iterative methods for solving linear systems.

关 键 词：Gauss-Seidel方法 预条件迭代法 Z-矩阵 

分 类 号：O241.6[理学—计算数学]