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2022年9月2日吴钢教授学术报告
上传时间:2022-09-02 作者: 浏览次数:10

报告题目: A Semi-randomized Kaczmarz Method with simple random sampling for large-scale linear systems 

报告人:吴钢 教授 

报告时间:2022.9.2 15:00-16:00 

报告地点:腾讯会议 566 537 118 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 iteration. So 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. To improve the semi-randomized Kaczmarz method further, inspired by Chebyshev’s 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 is free of computing residuals of the linear system, nor to construct index sets via scanning residuals. 

报告人简介:吴钢,博士,中国矿业大学数学学院教授、博士生导师,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:大规模科学与工程计算、数值代数、 机器学习与数据挖掘等。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 Matrix Analysis and Applications, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, Pattern Recognition, Machine Learning等期刊发表学术论文多篇。

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