一种循环分布的Guass-Seidel迭代算法求解线性方程组

A LOOP DISTRIBUTED GUASS-SEIDEL ITERATIVE ALGORITHM FOR SOLVING LINEAR EQUATIONS

针对基于工作站网络环境下,处理机的运算速度较快而处理机间的通信相对较慢的实际情况,给出了一种基于行循环分布的并行求解线性方程组的Guass-Seidel迭代算法。该算法将方程组的增广矩阵按行循环分布存储在各处理机中,循环传送每一次的迭代向量以减少处理器间的通信次数,同时,采用计算与通信部分重叠技术,提高并行算法的效率。同时用8台PC机联成局域网,在DebianLinux4.0操作系统、MPICH1.2.7并行计算平台上对该算法进行了数值实验,实验结果表明,该算法较传统的基于行带状分布的Guass-Seidel并行迭代算法优越。

With the consideration of actual circumstance that the speed of operation of processors is higher but the communication among processors is relatively lower in the environment based on network of workstations,a row loop distribution-based parallel Guass-Seidel iterative algorithm for solving linear equations is presented in this paper,in which the augmented matrix of equations is stored in local memories of all processors through row loop distribution,and the times of communication among the processors are decreased by loop-conveying each iterative vector.Meanwhile,this algorithm adopts the technology of overlapping computation and communication to improve the efficiency of the parallel algorithm.The results of numerical experiments,performed on parallel computing platform of a LAN made up of 8 personal computers with DebianLinux 4.0 operating system and MPICH 1.2.7,show that the algorithm presented in this paper is superior to the Guass-Seidel parallel iterative algorithm based on row zonal distribution.