USSOR方法应用于相容次序矩阵的收敛性

ON THE CONVERGENCE OF THE USSOR METHOD APPLIED TO THE CONSISTENTLY ORDERED MATRIX

本文的目的是讨论系数矩阵为相容次序矩阵的线性方程组Ａｘ＝ｂ．研究ＵＳＳＯＲ方法收敛性的充要条件以及最优收敛性质，给出最佳松驰因子表达式和ＵＳＳＯＲ迭代矩阵谱半径的上、下界。

The purpose of this paper is to disduss the linear system of equations Ax=b whose coefficient matrix is consistently ordered. We obtain the sufficient and necessary conditions of convergence, and the optimum convergence properties in the USSOR method. Also, we give the expression of all optimal relaxation factor and the bounds of the spectral radius of the USSOR iterative matrix.