An optimal eighth-order multipoint numerical iterative method to find simple root of scalar nonlinear equations

M. Z. Ullah
{"title":"An optimal eighth-order multipoint numerical iterative method to find simple root of\nscalar nonlinear equations","authors":"M. Z. Ullah","doi":"10.52280/pujm.2022.541103","DOIUrl":null,"url":null,"abstract":"An optimal eighth-order multipoint numerical iterative method is constructed to find the\nsimple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is\noptimal.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Punjab University Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52280/pujm.2022.541103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

An optimal eighth-order multipoint numerical iterative method is constructed to find the simple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is optimal.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
求标量非线性方程单根的最优八阶多点数值迭代法
构造了求标量非线性方程单根的最优八阶多点数值迭代方法。它是一种三点数值迭代法,使用与标量非线性方程及其导数之一f0(ⅱ)相关的函数f(ⅱ)的三次求值。这四个功能评价是实现八阶收敛所必需的。根据Kung-Traub猜想(KTC),无内存迭代数值多点方法的最大收敛阶数为2n±1,其中n为该方法在单个实例中函数求值的总次数。因此,遵循KTC,本文提出的方法是不优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Modification of Homotopy Perturbation Algorithm Through Least Square Optimizer for Higher Order Integro-Differential Equations Topological Descriptors and QSPR Models of Drugs used in Blood Cancer Analytical Method for Solving Inviscid Burger Equation Metric Based Fractional Dimension of Toeplitz Networks Translation Hypersurfaces in Euclidean 4-Spaces
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1