矩阵分裂的单调收敛性  

The Monotone Convergence of Splitting of Matrices

作　　者：宋永忠[1] 

机构地区：[1]南京师范大学数学系

出　　处：《应用数学》1989年第1期31-36,共6页Mathematica Applicata

摘　　要：本文在非负矩阵分裂条件下证明了迭代算法(3)的单调收敛性,它不仅推广了[1]～[5]中的相应结果,而且在比[7]中定理较弱的条件下,得到了广义AOR迭代法的单调收敛性。本文最后还给出了一个数值例子。The monotone convergences of regular splittings of matrices are well known in the analysis of iterative methods for solving large systems of linear equations. This article derives the monotone convergence of nonnegative splittings of matrices (i. e. A=M-N, where M^(-1) exists and M^(-1) N is nonnegative). And the corresponding results in [1-4] concerning regular splittings of matrices are special cases here. A monotone convergence theorem on the generalized AOR iterative method is given.

关 键 词：矩阵分裂 单调收敛性 迭代 

分 类 号：O241.6[理学—计算数学]