应数学与计算科学学院、广西应用数学中心(桂林电子科技大学)和广西高校数据分析与计算重点实验室邀请，中国矿业大学吴钢教授将于2022年12月17日下午15：00开始通过腾讯会议网络平台开展线上讲学，欢迎全校师生踊跃参加。报告具体安排如下：

题目：A Semi-Randomized Kaczmarz Method with Simple Random Sampling for Large-Scale Linear Systems

主讲人：吴钢教授

时间：2022年12月17日（周六）下午15：00-17:00

地点：腾讯会议（会议号：548-329-943）

摘要：Randomized Kaczmarz-type methods are appealing for large-scale linear systems arising from big-data problems. One of the keys of randomized Kaczmarz-type methods is how to effectively select working rows from the coefficient matrix. To the best of our knowledge, most of the randomized Kaczmarz-type methods need to compute probabilities for choosing working rows. However, when the amount of data is huge, the computation of probabilities will be inaccurate due to many factors such as rounding errors and data distribution.

Moreover, in some popular randomized Kaczmarz methods, we have to scan all the rows of the data matrix in advance, or to compute residual of the linear system in each step. Hence, we have to access all the rows of the data matrix, which are unfavorable for big-data problems. To overcome these difficulties, we first introduce a semi-randomized Kaczmarz method in which there is no need to compute probabilities explicitly. However, we still have to access all the rows of the matrix for the computation of residuals. To improve the semi-randomized Kaczmarz method further, inspired by Chebyshev's (weak) law of large numbers, we apply the simple sampling strategy to the semi-randomized Kaczmarz method, and propose a semi-randomized Kaczmarz method with simple random sampling. In the new method, there is no need to calculate probabilities explicitly and it is free of computing residuals of the linear system, and is free of constructing index sets via scanning residuals. Indeed, we only need to compute some elements of residuals corresponding to simple sampling sets, and a small portion of rows of the matrix are utilized. Convergence results are established to show the rationality and feasibility of the two proposed methods. Numerical experiments demonstrate the superiority of the new methods over many state-of-the-art randomized Kaczmarz methods for large-scale linear systems.

主讲人简介：

吴钢，中国矿业大学数学学院教授，博士研究生导师；江苏省“333工程”中青年科学技术带头人，江苏省“青蓝工程”中青年学术带头人，现任江苏省计算数学学会副理事长。主要研究方向：数值代数、机器学习与数据挖掘、大规模科学与工程计算等。先后主持国家自然科学基金项目、江苏省省自然科学基金项目多项，在国际知名杂志，如：SIAM Journal on Numerical Analysis, SIAM Journal on Matrix Analysis and Applications, SIAM Journalon Scientific Computing, IMA Journal of Numerical Analysis, IEEE Transactions on Knowledge and Data Engineering, Pattern Recognition, Machine Learning, ACM Transactions onInformation Systems等期刊发表学术论文多篇。