块TOR迭代法的收敛性

来源期刊：中南大学学报(自然科学版)2004年第1期

论文作者：向淑晃 张生雷

文章页码：171 - 174

关键词：线性方程组;块TOR迭代法;收敛性;块矩阵;谱半径

Key words：linear systems; block two-parameter overrelaxation method; convergence; block matrix;spectral radius

摘    要：

基于弱块对角占优矩阵与弱块H矩阵理论,利用最优尺度矩阵的方法给出了块TOR迭代法(BTOR迭代法)的收敛准则、迭代矩阵谱半径的上界估计式:若A为弱块H矩阵理论,则当α≥0,β≥0且0 <α+β<4/[1+ρ(|J (A)|]时,A的块TOR迭代法迭代矩阵谱半径满足:ρ(L_α,β,F(A))≤│1-[(α+β)/2]│+[(α+β)/2]ρ(│J(A)│)

Abstract:

By the theory of weak block diagonally dominant matrices and weak blockH-matrices,the block two-parameter overrelaxation (BTOR) methods are present, which generalized the TOR iterative methods for the solution of large linear systems.The convergence of BTOR iterative methods and some estimations about the spectral radius about BTOR methods are investigated in case thatA is a weak blockH-matrix:ifα≥0,β≥0, and 0<α+β<4/[1+ρ(|J^(A)|)], then ρ(L_α,β,F(A))≤│1-[(α+β)/2]│+[(α+β)/2]ρ(│J(A)│)