求解非对称线性方程组的s-BiCR算法  

The s-BiCR Algorithm to Solve Nonsymmetric Linear Systems

作　　者：仲妍[1] 骆志刚[1] 吴枫[1] 

机构地区：[1]国防科技大学计算机学院,湖南长沙410073

出　　处：《国防科技大学学报》2010年第2期61-67,共7页Journal of National University of Defense Technology

基　　金：国家部委基金资助项目(9140C8103050601)

摘　　要：在BiCR算法的基础上,提出了求解非对称线性方程组的s-BiCR算法。首先,给出了s-BiCR的基本计算框架,介绍了算法基本原理及参数求解方法;其次,通过分析s-BiCR中剩余向量与方向向量序列的基本性质,推导出减少参数求解计算量的方法,并在此基础上提出了一种更为高效的s-BiCR算法;最后,证明了s-BiCR的正确性,即在第i步产生的近似解与BiCR第is步产生的近似解是一致的,同时,通过性能分析发现,s-BiCR的同步通信次数与访存次数明显少于BiCR,说明该算法具有很好的并行特性和数据本地性。大量实验验证了s-BiCR的高效性和正确性。Based on the BiCR algorithm, s-BiCR algorithm is proposed to solve nonsymmetric linear systems. Firstly, the basic computation frame for the s-BiCR was given by introducing the fundamental principle in the new method and the solution approach to the parameters. Next, according to the analysis of the characters of the sequences of residual vectors and direction vectors, an approach is deduced to reduce computational volume for the parameters so that a more effective advanced s-BiCR is designed. Finally, the correctness of s-BiCR is proved, that is, the ith approximate solution from s-BiCR is equal to the isth approximate solution from BiCR. In ad- dition, by performance analysis, the number of both synchronous communication and accessing memory for s-BiCR is less than the one for BiCR so the algorithm here has better parallel feature and data locality. The effectivity and validity of s-BiCR have been confirmed by experiments.

关 键 词：非对称线性方程组 KRYLOV子空间 BiCR s-步方法 s-BiCR 

分 类 号：TP301[自动化与计算机技术—计算机系统结构] O241[自动化与计算机技术—计算机科学与技术]