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

被引：0

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.

引用

共 28 条

[1] KACZMARZ-TYPE INNER-ITERATION PRECONDITIONED FLEXIBLE GMRES METHODS FOR CONSISTENT LINEAR SYSTEMS\ast
Du, Yi-Shu
Hayami, Ken
Zheng, Ning
Morikuni, Keiichi
Yin, Jun-Feng
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2021, 43 (05): : S345 - S366
[2] Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems
Zhang, Xin-Fang
Xiao, Meng-Long
He, Zhuo-Heng
APPLIED MATHEMATICS LETTERS, 2025, 166
[3] CONVERGENCE OF INNER-ITERATION GMRES METHODS FOR RANK-DEFICIENT LEAST SQUARES PROBLEMS
Morikuni, Keiichi
Hayami, Ken
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (01) : 225 - 250
[4] On preconditioned iteration methods for complex linear systems
Zhong-Zhi Bai
Journal of Engineering Mathematics, 2015, 93 : 41 - 60
[5] On preconditioned iteration methods for complex linear systems
Bai, Zhong-Zhi
JOURNAL OF ENGINEERING MATHEMATICS, 2015, 93 (01) : 41 - 60
[6] Block sampling Kaczmarz–Motzkin methods for consistent linear systems
Yanjun Zhang
Hanyu Li
Calcolo, 2021, 58
[7] On preconditioned MHSS iteration methods for complex symmetric linear systems
Zhong-Zhi Bai
Michele Benzi
Fang Chen
Numerical Algorithms, 2011, 56 : 297 - 317
[8] On preconditioned MHSS iteration methods for complex symmetric linear systems
Bai, Zhong-Zhi
Benzi, Michele
Chen, Fang
NUMERICAL ALGORITHMS, 2011, 56 (02) : 297 - 317
[9] Block sampling Kaczmarz-Motzkin methods for consistent linear systems
Zhang, Yanjun
Li, Hanyu
CALCOLO, 2021, 58 (03)
[10] On fast greedy block Kaczmarz methods for solving large consistent linear systems
A.-Qin Xiao
Jun-Feng Yin
Ning Zheng
Computational and Applied Mathematics, 2023, 42

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