一类迭代法的统一收敛分析

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-07-24 DOI:10.1007/s11075-024-01893-x

Muniyasamy M, Santhosh George, Chandhini G

{"title":"一类迭代法的统一收敛分析","authors":"Muniyasamy M, Santhosh George, Chandhini G","doi":"10.1007/s11075-024-01893-x","DOIUrl":null,"url":null,"abstract":"<p>In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"68 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unified convergence analysis of a class of iterative methods\",\"authors\":\"Muniyasamy M, Santhosh George, Chandhini G\",\"doi\":\"10.1007/s11075-024-01893-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples.</p>\",\"PeriodicalId\":54709,\"journal\":{\"name\":\"Numerical Algorithms\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Algorithms\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11075-024-01893-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01893-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一类三阶、五阶和六阶迭代法的统一收敛分析，以求解巴拿赫空间环境下的非线性系统。我们的分析精确地给出了达到给定精度所需的迭代次数，以及利用相关算子的较弱条件得出的收敛球半径。我们通过各种数值示例来说明所提出的方法，并通过这些示例验证了理论上的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Unified convergence analysis of a class of iterative methods

查看原文本刊更多论文

Unified convergence analysis of a class of iterative methods

In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples.

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

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.