并行矩阵多分裂AOR算法的收敛性分析

Convergence Analysis of the Matrix Multisplitting AOR Algorithm

本文研究了求解大型线性代数方程组的并行矩阵多分裂AOR算法的收敛性态,并且给出了这类算法收敛与不收敛的充分条件.我们对这类算法的收敛速率做了估计,最后还给出了其单调收敛定理.

In this paper, we ste up several sufficient conditions ensuring the convergence as well as the divergence of the parallel matrix multisplitting AOR algorithm for solving large scale system of linear equations under proper constraints of the relaxed parameters and the multiple splittings by investigating this kind of method in detail. We estimate the convergence rate of this method and give its monotone convergence theorems.