一种改进的基于不完全分解的并行算法

The Improved Parallel Iterative Algorithm Based on Approximate Factorization

文章提出了一种基于不完全分解的大规模并行计算的带状线性方程组的并行迭代算法。为了并行迭代,对带状线性方程组的系数矩阵进行不完全近似分解,每次迭代仅仅相邻的CPU core之间进行通讯三次。Inspur TS10000集群服务器系统上测算了计算结果,表明该算法是可行的,并且具有良好的收敛性和效率。

In this paper,the improved parallel iterative algorithm for solving block-tridiagonal linear systems on distributed-memory multi-computers is presented. The coefficient matrix of the block-tridiagonal linear systems is approximately decomposed in order to perform the parallel computation,and an iterative scheme is formed. The communication needs only thrice between the adjacent processors all through the computing process at each iteration. Theoretically,a sufficient condition of convergence of the algorithm is given. Finally,the results of the experiments on Inspur TS10000 Cluster indicate that the algorithm is feasible with the preferable convergence and efficiency.