块三对角方程组的一种并行迭代解法

A New Algorithm Suitable for Parallel Computing in Solving Linear Equations Involving Block Tridiagonal Coefficient Matrix

给出了一种适合于分布式并行计算机的,解块三对角线性方程组的并行算法。该算法是通过给出分裂系数矩阵A的方式,再利用BAOR算法的迭代格式构造的,并从理论上证明了该算法的收敛速度和BAOR算法相同;通过给出的算例表明,实算与理论是一致的,同时该算法又具有BAOR算法所没有的良好的并行性。

BAOR (Block Accelerated Over-Relaxation) method, now commonly used in solving engineering problems involving block tridiagonal coefficient matrix, is not suitable for parallel computing. We now propose a new parallel algorithm that like BAOR algorithm, is good in convergence but, unlike BAOR algorithm, is suitable for parallel computing.In this paper we explain why BAOR algorithm is not suitable for parallel computing. This understanding helps us to make our algorithm suitable for parallel computing. We give one illustrative example. The iterative time needed by our new algorithm is roughly the same as that needed by BAOR algorithm. These results indicate preliminarily that our new algorithm is effective and feasible.