求解大型线性系统的K-均值最大残差块方法  

K-Means Maximum Residual Block Method for Solving Large Linear Systems

作　　者：黄柏顺 

机构地区：[1]温州大学数理学院,浙江 温州

出　　处：《应用数学进展》2024年第11期5063-5072,共10页Advances in Applied Mathematics

摘　　要：求解大型线性系统,带K-均值聚类的贪婪随机块Kaczmarz方法是近几年被广受关注的一类方法。本文在该方法基础上做了进一步的研究即在每一次迭代中优先消除残差向量中的最大块,构建了最大残差块Kaczmarz方法及其加速版本并进行了收敛性分析。数值实验证实了本文算法的有效性。The greedy random block Kaczmarz method with K-means clustering for solving large linear systems has been widely studied in recent years. This article conducted further research on this method by prioritizing the elimination of the largest block in the residual vector in each iteration, constructing the Kaczmarz method for the maximum residual block and its accelerated version, and conducting convergence analysis. Numerical experiments have confirmed the effectiveness of the algorithm proposed in this paper.

关 键 词：一致线性系统 最大残差块Kaczmarz K-均值算法 收敛性质 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]