多参数超松驰并行二阶段多分裂迭代算法

Multi-parameters Overelaxation Parallel Two-stage Multisplitting Iterative Methods

本文提出求解线性方程组的多参数超松弛并行二阶段多分裂迭方法 ,讨论了多参数的选取范围 .当系数矩阵是 M—矩阵或 H—矩阵时 ,且多参数的选取范围满足 0 <wi≤ w<21 +ρ(|J|) ,这里 J是 Jacobi迭代矩阵 ,该方法被证明是收敛的 .最后较详细地研究了多参数的 SOR方法 ,给出了多参数的收敛范围 .

In this paper, we propose multi parameters overelaxation parallel two stage multisplitting iterative methods for the parallel solution of linear algebraic systems, and discuss the region of multi parameter factors. Convergence theories are given when the confficient matrix is either an M matrix or an H matrix and multi parameter factors w i (i=1,2,…,α) satisfy 0<w i≤w<21+ρ(|J|) , where J is Jacopi iteration matrix. Finally, we also study multi parameters SOR iterative methods, and give the region of multi parameters w i (i=1,2,…,α).