【摘要】 提出了一种在MIMD分布式存储环境下求解带状线性方程组的交替方向迭代并行算法。利用系数矩阵的结构特点分裂矩阵,使整个计算过程只在相邻处理机间通信两次。给出了系数矩阵分别为Hermite正定矩阵和M-矩阵时算法收敛的充分条件。最后,在HP rx2600集群系统上进行的数值计算表明,该算法与多分裂方法相比具有较高的加速比和并行效率。更多还原

【Abstract】 The work presented in this paper focused on alternating-direction parallel iterative method for solving banded-linear systems on distributed-memory multi-computers.Firstly,the matrix was splitted by using the feature of the coefficient matrix,thus the communication only need twice between the adjacent processors per iteration step.Furthermore,the sufficient conditions for convergence were given when the coefficient matrix A is a Hermite positive definite matrix or M-matrix respectively.Finally,the numerical experiments implemented on HP rx2600 cluster indicate that the algorithm’s parallel acceleration rates and efficiency are higher than the multi-splitting method’s.更多还原