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2019-09-17 Bai教授による数値解析講演会

投稿者:  速水 謙(国立情報学研究所)
会場: 国立情報学研究所 12F, Room 1212 (Lecture Room 1)
概要: Lecture on Numerical Analysis "Recent Advances on the Randomized Kaczmarz Method"

日程 2019年 9月17日(火) 11:00-12:00 /
September 17th (Tuesday) 11:00-12:00
会場 国立情報学研究所 12F, Room 1212 (Lecture Room 1) /
National Institute of Informatics, 12F, Room 1212 (Lecture Room 1)
(access)
Title Recent Advances on the Randomized Kaczmarz Method
Speaker Professor Zhong-Zhi Bai
State Key Laboratory of Scientific/Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing, P.R. China
Abstract For solving large scale system of linear equations by iteration methods, we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a greedy randomized Kaczmarz method. It is proved that this method converges to the unique least-norm solution of the linear system when it is consistent. Theoretical analysis demonstrates that the convergence rate of the greedy randomized Kaczmarz method is much faster than the randomized Kaczmarz method, and numerical results show that the greedy randomized Kaczmarz method is more efficient than the randomized Kaczmarz method, too. In addition, by introducing a relaxation parameter in the involved probability criterion, we further generalize the greedy randomized Kaczmarz method, obtaining a class of relaxed greedy randomized Kaczmarz methods. Both theoretical validation and numerical verification show that these methods can be more efficient than the greedy randomized Kaczmarz method if the relaxation parameter is chosen appropriately.
問い合わせ先 速水 謙
〒101-8430 東京都 千代田区 一ツ橋 2-1-2 国立情報学研究所
e-mail: hayamiseparatornii.ac.jp