学术报告：杨爱利 教授（海南师范大学）

主讲人：杨爱利 教授（海南师范大学）

题目：K-means clustering based maximal residual (block) Kaczmarz methods for solving large scale system of linear equations

时间：2025年5月24日上午11：20—11：50

地点：肇庆学院行政楼第二会议室

Abstract: In recent years, the Kaczmarz method has garnered wide attention for solving large-scale consistent system of linear equations due to its minimal storage requirements. To effectively enhance the efficiency of the Kaczmarz method, we employ k-means clustering method to partition all equations (or equivalently, hyperplanes) into k clusters. Subsequently, in each iteration, the approximate solution is updated using the equation with the maximum residual within a randomly selected cluster, thereby constructing a k-means clustering based randomized maximum residual Kaczmarz (abbreviated as RMRK(k)) method. To further enhance the computational efficiency, a maximum residual block Kaczmarz method with k-means clustering (abbreviated as MRBK(k)) is constructed by simultaneously updating the approximate solution using the equations with the maximum residuals within each cluster. The convergence of both methods is rigorously proved, demonstrating that for any chosen initial value in the column space of coefficient matrix, the iterative sequences generated by both methods converge unconditionally to the minimum-norm solution of the linear system. Numerical experimental results validate the feasibility and effectiveness of these two methods.

报告人简介:海南师范大学教授，博士生导师，科学技术院副院长。2008年在兰州大学获得理学博士学位。2010-2011年新加坡国立大学博士后。主要从事大型稀疏线性系统的快速算法设计及分析的研究工作。主持国家自然科学基金3项、省自然科学基金2项、省级教学研究项目1项，参加国家重点研发计划和新加坡-麻省理工联盟科技项目各1项。迄今为止，在BIT Numer.Math., Numer.Linear. Algebra Appl., Appl.Math.Model.等期刊发表SCI论文50余篇，2篇入选ESI高被引论文，发表在Numer. Linear Algebra Appl.上的论文被该刊评为2018和2019年度Top cited article. 另外，还担任J. Sci. Comput.， Appl. Math. Letters., Numer.Algorithms等十余种SCI期刊的审稿人。