Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Xin-Fang Zhang , Meng-Long Xiao , Zhuo-Heng He
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引用次数: 0

Abstract

Kacamarz-type inner-iteration preconditioned flexible GMRES method, which was proposed by Du et al. (2021), is attractive for solving consistent linear systems. However, its inner iteration was only performed by several commonly used Kaczmarz-type methods, and required computing AAT in advance, which is unfavorable for big data problems. To overcome these difficulties, we first propose a simple orthogonal block Kaczmarz method, based on the orthogonal block idea without preconditioning, which converges much faster than the mentioned-above Kaczmarz-type solvers. We then derive a simple orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method, based on the orthogonal block Kaczmarz inner-iteration as a preconditioner, which is appealing for large-scale linear systems. The convergence analysis of which is also established. Finally, we provide some numerical examples to illustrate the effectiveness of the proposed methods compared with some state-of-the-art Kaczmarz-type methods.
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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