求解块三对角线性方程组的一种并行算法  

A parallel algorithm for solving block-tridiagonal linear equations

作　　者：汪保[1] 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

出　　处：《纺织高校基础科学学报》2008年第1期93-98,共6页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金资助项目(2005A16)

摘　　要：提出了分布式环境下求解块三对角线性方程组的一种并行混合迭代算法.利用分裂系数矩阵的方式,产生一个简单迭代;然后再利用多方向搜索方法,使得多方向搜索方法收敛速度加快.该算法只在相邻处理机间通信4次,消除了共轭梯度法所需要的内积运算.从理论上给出了算法收敛的一个充分条件.在HP rx2600集群上进行了数值试验,结果表明,实算与理论是一致的,并行效率也很高且比相关文献的计算效果好.A parallel algorithm for block-tridiagonal linear equations on distributed-memory multi-computers was presented. The algorithm produced iterative method by splitting the coefficient matrix and then used multiple search directions to solve the linear system. The communication is only four times between the adjacent processors. This method eliminate global inner product entirely. In theory, an enough condition for converge of the algorithm is given. Finally, some numerical results on HP rx2600 cluster show that practice computing is consistent with theory. The algorithm＇s parallel effidency is high.

关 键 词：块三对角线性方程组 并行算法 HP rx2600集群 

分 类 号：O246[理学—计算数学]