求解相容线性方程组的贪婪块Kaczmarz方法  

GREEDY BLOCK KACZMARZ METHOD FOR SOLVING CONSISTENT LINEAR EQUATION SYSTEMS

作　　者：孙超 郭晓霞[1] Sun Chao;Guo Xiaoxia(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,青岛266100

出　　处：《数值计算与计算机应用》2024年第3期237-248,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11871444)资助。

摘　　要：本文首先针对文献[14]中的贪婪Kaczmarz (GK)方法提出了一个新的收敛定理;其次,为了提高求解相容线性方程组的效率,基于GK方法的贪婪策略提出了一种新的贪婪块Kaczmarz(RDBK)方法,并给出了RDBK方法的收敛定理;最后,数值实验表明RDBK方法在迭代步数和计算时间方面均显著优于GK方法.In this paper,we first provide a new convergence theorem for the greedy Kaczmarz(GK)method in reference[14].Secondly,in order to improve the efficiency of solving consistent linear equations,a new greedy block Kaczmarz(RDBK)method based on the greedy strat-egy of the GK method is proposed,and the convergence theorem of the RDBK method is provided.Finally,the numerical results demonstrate that the RDBK method is significantly superior to the GK method in terms of iteration steps and computation time.

关 键 词：收敛性 贪婪策略 线性方程组 Kaczmarz方法 残差 

分 类 号：O241.6[理学—计算数学]