块三对角线性方程组的并行迭代解法  

A new parallel iterative algorithm for solving block-tridiagonal linear equations

作　　者：樊艳红[1,2] 吕全义[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072 [2]西北工业大学航空学院,陕西西安710072

出　　处：《纺织高校基础科学学报》2010年第2期174-179,共6页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金资助项目(2006A05)

摘　　要：提出了一种求解系数矩阵为块三对角矩阵的线性方程组的适合于MIMD分布式存储的并行迭代算法.该算法将一个分块三对角线性方程组的系数矩阵进行适合并行计算的不完全分解,从而形成迭代格式.整个计算过程只在相邻处理机之间进行3次通信.并从理论上给出了该算法收敛的一个充分条件,最后在HP rx2600集群上进行了数值实验.结果表明,此算法是可行的,具有较好的收敛性与并行效率.The parallel iterative algorithm for solving block-tridiagonal linear equations on a distributed-memory multi-computers is presented.The coefficient matrix of the block-tridiagonal linear systems is incompletely decomposed in order to adapt the parallel computation,then the iterative scheme is obtained.The communication is only third between the adjacent processors all through the computing process.Theoretically,the sufficient condition of convergence of the algorithm is demonstrated.Finally,the results of the experiments on HP rx2600 cluster indicate the algorithm is feasible with the preferable convergence and the effective efficiency.

关 键 词：块三对角线性方程组 并行算法 LU分解 HP rx2600集群 

分 类 号：O151.21[理学—数学] TP301[理学—基础数学]