基于新预条件因子的修正Gauss-Seidel法  

An improved Gauss-Seidel method based on a new preconditioner

作　　者：陈金雄[1] 陈光喜[1] 石艳超[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林514004

出　　处：《云南大学学报（自然科学版）》2008年第S2期128-132,138,共6页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10661005;10501009)

摘　　要：首先提出了解线性方程组Ax=b的一种新预条件因子,并运用到Gauss-Seidel方法中.其次,证明了对于不可约的L-矩阵,新的预条件方法可以加速修正Gauss-Seidel法,并对相应迭代矩阵的谱半径做了比较和给出了收敛最快时的系数取值.数值例子说明提出的预条件Gauss-Seidel法是有效的.Firstly,a new preconditioner of solving the linear system Ax=b is presented,and the preconditioner is applied to Gauss-Seidel method.Secondly,it is shown that the new preconditioned method can accelerate the improving Gauss-Seidel for irreducible L-matrices.Some comparison theorems between the spectral radiuses of corresponding iterative matrices and the optimal parmeter are given.Its validity is illustrated by some numerical exampled.

关 键 词：预条件因子 Gauss-Seidel方法 谱半径 L-矩阵 

分 类 号：O241.6[理学—计算数学]