On the convergence of Homeier method and its extensions

被引：0
|
作者：
K. Muhammed Saeed
R. Krishnendu
Santhosh George
Jidesh Padikkal
机构：
[1] National Institute of Technology Karnataka,Department of Mathematical and Computational Sciences
来源：
The Journal of Analysis | 2023年 / 31卷
关键词：
Homeier method; Convergence order; Taylor expansion; Iterative methods; Banach space; 41A25; 49M15; 65D99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A third-order Homeier method for solving equations in Banach space is studied. Using assumptions on the first and second derivatives, we obtained third-order convergence. Our technique does not involve Taylor series expansion and can be extended to similar higher-order methods. We have given two extensions of the method with orders five and six. Examples with radii of convergence and basins of attraction are provided.
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页码：645 / 656
页数：11
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