A two-parameter third-order family of methods for solving nonlinear equations

Changbum Chun

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A two-parameter third-order family of methods for solving nonlinear equations

机译：求解非线性方程的两参数三阶方法族

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摘要

In this paper, we present a new two-parameter family of iterative methods for solving nonlinear equations which includes, as a particular case, the classical Potra and Pták third-order method. Per iteration the new methods require two evaluations of the function and one evaluation of its first derivative. It is shown that each family member is cubically convergent. Several examples are given to illustrate the performance of the family members.

机译：在本文中，我们提出了一种新的两参数迭代方法，用于求解非线性方程，其中，在特定情况下，包括经典的Potra和Pták三阶方法。每次迭代，新方法都需要对该函数进行两次评估，并对其一阶导数进行一次评估。结果表明，每个家庭成员都是三次收敛的。举几个例子来说明家庭成员的表现。

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《Applied mathematics and computation》 |2007年第2期|共6页
作者
Changbum Chun;
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正文语种 eng
中图分类应用数学;
关键词
Newton’s method; Iterative methods; Nonlinear equations; Order of convergence;

机译：牛顿法;迭代法;非线性方程;收敛阶;

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专利

1. A two-parameter third-order family of methods for solving nonlinear equations [J] . Changbum Chun Applied mathematics and computation . 2007,第2期

机译：求解非线性方程的两参数三阶方法族
2. Some third-order families of iterative methods for solving nonlinear equations [J] . Chun C Applied mathematics and computation . 2007,第1期

机译：求解非线性方程的一些三阶迭代方法
3. A one-parameter family of third-order methods to solve nonlinear equations [J] . Changbum Chun Applied mathematics and computation . 2007,第1期

机译：解非线性方程的单参数三阶方法族
4. A Two-Parameter Family of Combined Iterative Methods for Solving Nonlinear Equations [C] . Xueliang Zheng, Shuping Chen CSO 2010;International joint conference on computational sciences and optimization . 2010

机译：求解非线性方程的两参数组合迭代方法
5. Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers*. [D] . Bouaricha, Ali. 1992

机译：在连续和并行计算机上使用张量法来求解非线性方程和非线性最小二乘问题的大型稀疏系统。
6. On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations [O] . Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, -1

机译：基于Bi等人的概论。八阶收敛迭代法求解非线性方程
7. A New Class of Halley’s Method with Third-Order Convergence for Solving Nonlinear Equations [O] . Mohammed Barrada, Mariya Ouaissa, Yassine Rhazali, 2020

机译：具有用于求解非线性方程的三阶收敛的新一类哈利方法

A two-parameter third-order family of methods for solving nonlinear equations

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