求解大型稀疏线性方程组的贪婪距离随机Kaczmarz方法  

Greedy Randomized-Distance Kaczmarz Method for Solving Large Sparse Linear Systems

作　　者：杜亦疏 殷俊锋[1] 张科 DU Yishu;YIN Junfeng;ZHANG Ke(School of Mathematical Sciences,Tongji University,Shanghai 200092,China;College of Arts and Sciences,Shanghai Maritime University,Shanghai 201306,China)

机构地区：[1]同济大学数学科学学院,上海200092 [2]上海海事大学文理学院,上海201306

出　　处：《同济大学学报（自然科学版）》2020年第8期1224-1231,1240,共9页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金面上项目(11971354);国家自然科学基金(11601323)。

摘　　要：基于一种从系数矩阵中选取工作行的新概率准则提出一类求解大型稀疏线性方程组的贪婪距离随机Kaczmarz方法.理论表明该方法收敛到相容线性方程组的最小范数解,而且该方法的理论收敛因子小于经典随机Kaczmarz方法的收敛因子.数值实验表明该方法比传统的随机Kaczmarz方法收敛更快.Based on a new probability criterion to select the working rows from the coefficient matrix,a greedydistance randomized Kaczmarz method was proposed to solve large sparse linear systems.The theoretical analysis demonstrates that this method converges to the leastnorm solution when the linear system is consistent,and the convergence factor of the greedy-distance randomized Kaczmarz method is smaller than that of the randomized Kaczmarz method.Moreover,the numerical results have verified its effectiveness.

关 键 词：Kaczmarz方法 稀疏线性方程组 收敛性 随机迭代 

分 类 号：O241.6[理学—计算数学]