求解非线性方程组的一组七阶和八阶收敛的牛顿型方法

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-01-01 DOI:10.15672/hujms.1061471

T. Zhanlav, Renchin-Ochir Mijiddorj, Otgondorj Khuder

{"title":"求解非线性方程组的一组七阶和八阶收敛的牛顿型方法","authors":"T. Zhanlav, Renchin-Ochir Mijiddorj, Otgondorj Khuder","doi":"10.15672/hujms.1061471","DOIUrl":null,"url":null,"abstract":"In this work, we first develop a new family of three-step seventh and eighth-order Newton-type iterative methods for solving systems of nonlinear equations. We also propose some different choices of parameter matrices that ensure the convergence order. The proposed family includes some known methods of special cases. The computational cost and efficiency index of our methods are discussed. Numerical experiments give to support the theoretical results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"24 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A family of Newton-type methods with seventh and eighth-order of convergence for solving systems of nonlinear equations\",\"authors\":\"T. Zhanlav, Renchin-Ochir Mijiddorj, Otgondorj Khuder\",\"doi\":\"10.15672/hujms.1061471\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we first develop a new family of three-step seventh and eighth-order Newton-type iterative methods for solving systems of nonlinear equations. We also propose some different choices of parameter matrices that ensure the convergence order. The proposed family includes some known methods of special cases. The computational cost and efficiency index of our methods are discussed. Numerical experiments give to support the theoretical results.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1061471\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1061471","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在这项工作中，我们首先开发了一种新的三步七阶和八阶牛顿型迭代方法，用于求解非线性方程组。我们还提出了保证收敛顺序的参数矩阵的几种不同选择。建议的家庭包括一些已知的特殊情况的方法。讨论了这些方法的计算成本和效率指标。数值实验结果支持了理论结果。

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

A family of Newton-type methods with seventh and eighth-order of convergence for solving systems of nonlinear equations

In this work, we first develop a new family of three-step seventh and eighth-order Newton-type iterative methods for solving systems of nonlinear equations. We also propose some different choices of parameter matrices that ensure the convergence order. The proposed family includes some known methods of special cases. The computational cost and efficiency index of our methods are discussed. Numerical experiments give to support the theoretical results.

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

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.