一种改进的变预处理SOR-BICR算法  

An Improved Variable Preconditioning SOR-BICR Algorithm

作　　者：刘广西 张衡 LIU Guangxi1, ZHANG Heng2(1 .School of Mathematics and Information, Fujian Normal University, Fuzhou, Fujian, 350007, China;2.Fuqing Branch of Fujian Normal University, Fuqingf Fujian 350300, China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117 [2]福建师范大学福清分校电子与信息工程学院,福建福清350300

出　　处：《福建师大福清分校学报》2018年第2期1-6,共6页Journal of Fuqing Branch of Fujian Normal University

基　　金：福建省自然科学基金(2014J01006)

摘　　要：为了在分布式并行环境中求解大型稀疏线性方程组,对变预处理SOR-双共轭残量算法(简称SOR-BICR)的计算次序进行重构进而得到改进的变预处理子SOR-双共轭残量(简称SOR-IBICR)算法,SOR-双共轭残量算法中的两个全局同步点,而在SOR-IBICR算法中只有一个全局同步点,同时内积计算所需要的通讯是可以与向量校正的计算时间有效地重叠.通过理论分析表明,相对变预处理变预处理SOR-双共轭残量算法而言,SOR-IBICR算法有着更好的并行性能和可扩展性能.In order to solve large sparse linear equations in distributed parallel environment, the calculation order of variable preconditioning SOR-BICR is reconstructed into SOR-IBICR algorithm. While there are two global synchronized points in SOR-IBICR, there is only one in SOR-BICR. Meanwhile the communication needed to calculate the inner product can effectively overlap with the time for vector correction. The theoretical analysis shows that the variable preconditioning SOR-IBICR algorithm has better parallelism and extensibility than the variable preconditioning SOR-BICR.

关 键 词：KRYLOV子空间 变预处理SOR-BICR算法 同步开销 全局通信 大型稀疏线性方程组 

分 类 号：O241.6[理学—计算数学]