On the Optimal Choice of Parameters in Two-Point Iterative Methods for Solving Nonlinear Equations

被引：0
|
作者：
Zhanlav, T. [1 ]
Otgondorj, Kh [1 ,2 ]
机构：
[1] Mongolian Acad Sci, Inst Math & Digital Technol, Ulan Bator 13330, Mongolia
[2] Mongolian Univ Sci & Technol, Sch Appl Sci, Ulan Bator 14191, Mongolia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2021年 / 61卷 / 01期
关键词：
nonlinear equations; two-point iterations; methods with memory; optimal methods; HANSEN-PATRICKS FAMILY; MEMORY;
D O I：
10.1134/S0965542520120180
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new optimal two-parameter class of derivative-free iterative methods with the application to the Hansen-Patrick type iterations is developed. Using self-accelerating parameters, new higher order methods with memory are obtained. Exact analytical formulas for the optimal values of the parameters are found for the first time. The convergence order is increased from four to seven without any additional computations. Thus, the proposed methods with memory have a high computational efficiency. Numerical examples and comparison with some other available methods confirm the theoretical results and high computational efficiency.
引用
收藏
页码：29 / 42
页数：14
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