求解大型稀疏线性系统的改进带残差的部分随机扩展Kaczmarz方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-11 DOI:10.1016/j.apnum.2025.02.004

Chen-Xiao Gao, Fang Chen

{"title":"求解大型稀疏线性系统的改进带残差的部分随机扩展Kaczmarz方法","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":2.2000,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":2.2000,\"publicationDate\":\"2025-02-11\",\"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\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","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":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

带残差的部分随机扩展Kaczmarz方法是求解大型稀疏线性系统的有效方法。本文提出了该方法的一种改进形式，并证明了其预期的指数收敛速度。此外，数值结果表明，该方法优于带残差的部分随机扩展Kaczmarz方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Modified partially randomized extended Kaczmarz method with residual for solving large sparse linear systems

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

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.