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

Zhanlav T.; Otgondorj Kh

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

机译：求解非线性方程的两点迭代方法参数的最优选择

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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.

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来源
《Computational mathematics and mathematical physics》 |2021年第1期|共14页
作者
Zhanlav T.; Otgondorj Kh;
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作者单位

Mongolian Acad Sci Inst Math &

Digital Technol Ulan Bator 13330 Mongolia;

Mongolian Acad Sci Inst Math &

Digital Technol Ulan Bator 13330 Mongolia;

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原文格式 PDF
正文语种 eng
中图分类计算数学;
关键词
nonlinear equations; two-point iterations; methods with memory; optimal methods;

机译：非线性方程;两点迭代;内存的方法;最优方法;

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2. PARAMETER ITERATION METHOD FOR SOLVING NONLINEAR PROBLEM [J] . 林建国应用数学和力学（英文版） . 2001,第007期
3. An optimal order a posteriori parameter choice strategy with modified Newton iterative scheme for solving nonlinear ill-posed operator equations [J] . Pradeep D., Rajan M. P. International journal of computing science and mathematics . 2017,第4期

机译：修正牛顿迭代法的最优阶后验参数选择策略求解非线性不适定算子方程
4. Several two-point with memory iterative methods for solving nonlinear equations [J] . Neha Choubey, Bhavna Panday, J. P. Jaiswal Afrika matematika . 2018,第3a4期

机译：具有内存迭代方法的几个两点，用于求解非线性方程
5. Two-point iterative methods for solving nonlinear equations [J] . Abu-Alshaikh I, Sahin A Applied mathematics and computation . 2006,第1期

机译：求解非线性方程的两点迭代法
6. One-Parameter Third-Order Iterative Methods for Solving Nonlinear Equations [C] . An Jie, Yuan Yuan Fourth international conference on information and computing . 2011

机译：解非线性方程的一参数三阶迭代方法
7. AN ITERATIVE METHOD FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS WITH DYNAMIC ESTIMATION OF PARAMETERS. [D] . MANTEUFFEL, THOMAS ALBERT -1

机译：参数动态估计的非对称线性系统求解的一种迭代方法。
8. Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations [O] . Na Huang, Changfeng Ma -1

机译：求解非线性方程组的不动点迭代法的收敛性分析和数值研究
9. A multi-point iterative method for solving nonlinear equations with optimal order of convergence [O] . Mehdi Salimi, N. M. A. Nik Long, Somayeh Sharifi, 2018

机译：一种多点迭代方法，用于求解收敛最佳阶数的非线性方程
10. On the Optimal Choice of Nodes in the C-P Method for Solving Linear Operator Equations. [R] . wahba,grace 1974

机译：求解线性算子方程的C-p方法中节点的最优选择。

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

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