{"title":"Modified partially randomized extended Kaczmarz method with residual for solving large sparse linear systems","authors":"Chen-Xiao Gao, Fang Chen","doi":"10.1016/j.apnum.2025.02.004","DOIUrl":null,"url":null,"abstract":"<div><div>The partially randomized extended Kaczmarz method with residual is effective for solving large sparse linear systems. In this paper, an improved variant of this method is proposed and its expected exponential convergence rate is proved. In addition, numerical results show that this method can preform better than the partially randomized extended Kaczmarz method with residual.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 215-222"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927425000285","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/11 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The partially randomized extended Kaczmarz method with residual is effective for solving large sparse linear systems. In this paper, an improved variant of this method is proposed and its expected exponential convergence rate is proved. In addition, numerical results show that this method can preform better than the partially randomized extended Kaczmarz method with residual.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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