求解块三对角线性方程组的含参并行算法

Parametric parallel algorithm for solving block-tridiagonal linear equations

提出了分布式环境下求解含有两个参数的矩阵分裂方式的一种交替方向迭代并行算法,通过引入两个参数并巧妙分解系数矩阵A得到新算法,从理论上给出了该算法收敛的两个充分条件,并讨论了参数的选择范围。基于局域网的MPI异构环境,在HP rx2600集群上进行了数值实验,并与多分裂方法比较。比较的结果表明,此算法是可行的,具有良好的并行效率。

An alternate direction iterative parallel algorithm for block-tridiagonal linear equations is presented. The one is suit for distributed-memory multi-computer. By introducing two parameters and splitting the coefficient matrix A skillfully, a new algorithm is obtained. According to theoretical analysis, two sufficient conditions of the algorithm convergence and scopes about the parameters are given. Finally, the results of numerical experiments on HP rx2600 cluster by the algorithm on MPI environment based on local net and by the multi-splitting method indicate that the algorithm is feasible and it has highly parallel efficiency.