解大规模线性方程组的Mann迭代并行算法

MANN ITERATION'S PARALLEL AIGORITHM FOR SOLVING LARGE-SCALE LINEAR SYSTEMS OF EQUATIONS

利用实函数不动点的Mann迭代算法,提出了一种求解大规模线性方程组新的并行算法,分析了算法的并行加速比,讨论了算法在基于消息传递机制的MPI并行环境下的实现流程,给出了并行环境上的实验。该算法适用范围广,数值计算结果表明理论分析与实际计算相符合,算法在并行环境下具有较好的并行度,可适合大规模科学与工程的高性能计算。

A new parallel algorithm for solving large-scale linear systems of equations is suggested by using Mann iteration which is one of the fixed point iterations for real functions. In this paper it describes the algorithm, analyzes its parallel speedup ratio, and discusses its realising procedure in MPI parallel environment based on information passing mechanism with the experiments in the environment. As a widely suitable algorithm, numerical results show that its theoretic analysis coincide with the actual computations, and has fairly good parallelism in parallel environment, and can be used in large-scale high performance computations arising from scientific and engineering computing.