KACZMARZ-TYPE INNER-ITERATION PRECONDITIONED FLEXIBLE GMRES METHODS FOR CONSISTENT LINEAR SYSTEMS

被引：0
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作者：
Du Y.-S. [1 ,2 ]
Hayami K. [3 ]
Zheng N. [4 ]
Morikuni K. [5 ]
Yin J.-F. [1 ]
机构：
[1] School of Mathematical Sciences, Tongji University, N.O. 1239, Siping Road, Shanghai
[2] LIP, École Normale Supérieure de Lyon, INRIA, 46 Allée d'Italie, Lyon
[3] National Institute of Informatics, The Graduate University for Advanced Studies (SOKENDAI), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo
[4] Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo
[5] Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Ibaraki, Tsukuba
来源：
Du, Yi-Shu (duyishu@tongji.edu.cn) | 1600年 / National Institute of Informatics卷 / 2020期
基金：
日本学术振兴会; 中国国家自然科学基金;
关键词：
flexible GMRES; GMRES; inner-outer iteration; iterative method; Kaczmarz method; least squares problem; linear system; overdetermined system; preconditioner; randomized algorithm; underdetermined system;
D O I：
10.48550/arXiv.2006.10818
中图分类号：
学科分类号：
摘要：
We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter. We also present theoretical justifications of the right-preconditioned flexible GMRES for solving consistent linear systems. Numerical experiments on overdetermined and underdetermined linear systems show that the proposed method is superior to the GMRES method preconditioned by NE-SOR inner iterations in terms of total CPU time. © 2020 National Institute of Informatics. All rights reserved.
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