病态线性方程组的并行迭代求解  

Parallel iterative method for solving ill-conditioned linear equations

作　　者：黄丽嫦[1] 林结[1] 黄润[2] 

机构地区：[1]佛山职业技术学院基础教学部,广东佛山528137 [2]佛山职业技术学院电子信息系,广东佛山528137

出　　处：《佛山科学技术学院学报（自然科学版）》2016年第4期13-17,共5页Journal of Foshan University(Natural Science Edition)

基　　金：佛山职业技术学院校级科研基金资助项目(KY2013Y07)

摘　　要：分析了病态线性方程组的相关概念及判别方法,给出了一种病态线性方程组并行迭代的求解算法。算法首先对病态线性方程组的系数矩阵进行严格对角占优预处理,在此基础上,用并行的Jacobi迭代法进行多步迭代求解。新算法易于在多核架构的微机中实现,且数值实验也验证了算法具有良好的收敛性和并行性。This paper analyzes the concepts a nd discriminatimg methods of ill-conditioned linear equations,presents a parallel iterative algorithm. The pretreatment algorithm based on ill conditioned coefficient matrix ofthe linear equations is strictly diagonally dominant, based on multi step iterative m ethod for solving the equationsafter pretreatment with parallel Jacobi iterative method . Thenew algorithm is easy to implement on computermulti-core architecture, and the numerical experiments show that the algorithm has good convergence andparallelism.

关 键 词：病态线性方程组 并行计算 雅可比迭代法 

分 类 号：O241.6[理学—计算数学]