Abstract: This paper presents an alternating-direction iterative algorithm for solving banded linear equations on distributed-memory multi-computers.Authors make full use of the special structure characteristics of the coefficient matrix，give sufficient conditions of Hermite positive definite matrix and M-matrix，and discuss interval of convergence of the parameters for splitting mode.Finally，some examples results on HP rx2600 cluster show that it is consistent with convergence theory.The numerical experiments indicate that the algorithm is feasible and effective and has good parallelism.

Key words: alternating-direction iterative algorithm, HP rx2600 cluster, parallelism

摘要： 提出了分布式存储环境下求解带状线性方程组的并行交替方向迭代算法。充分利用系数矩阵的结构特点，给出了在系数矩阵分别为Hermite正定矩阵和M-矩阵时算法的充分条件，并针对采用的分裂方式，讨论了参数的收敛范围，最后在HP rx2600集群系统上进行了数值计算，结果表明实算与理论相一致，算法简便可行且具有良好的并行性。

关键词: 交替方向法, HP rx2600集群, 并行性