On randomized explicit block Kaczmarz method for solving large linear systems

：苗存强（中南大学）
：2026-04-25 10:30
：海韵园行政楼C503

报告人：苗存强（中南大学）

时  间：2026年4月25日10:30

地  点：海韵园行政楼C503

内容摘要:

The randomized block Kaczmarz method (Linear Algebra Appl., 441: 199-221, 2014) proposed by Needell and Tropp is efficient for solving large consistent linear systems. However, each iteration of the randomized block Kaczmarz method carries a high cost, as it calls for the computation of a pseudoinverse, or equivalently, the solution of a least-squares problem. In this talk, we propose a randomized explicit block Kaczmarz method that avoids the direct computation of pseudoinverses by exploiting the structure of the block updates. This explicit formulation allows for a more flexible selection of the rows in the working block at each iteration, without relying on a predefined partition of the row indices. Based on a randomized block selection strategy, we further establish the convergence properties of the proposed method. It indicates that the randomized explicit block Kaczmarz method exhibits faster convergence compared to the multi-step standard randomized Kaczmarz method and the randomized block Kaczmarz method. Finally, numerical experiments are carried out to show great superiority and robustness over some state-of-the-art randomized block Kaczmarz methods.

个人简介：

苗存强，中南大学数学与统计学院副教授，研究方向为数值代数，致力于代数特征值及线性方程组迭代算法的构造及理论分析，主要研究成果发表在Advances in Computational Mathematics, Journal of Scientific Computing等期刊。主持完成国家自然科学基金青年项目及湖南省自然科学基金面上项目等。

 

联系人：谭志裕