Some second-derivative-free variants of Halley's method for multiple roots

Li SG; Li HS; Cheng LZ

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Some second-derivative-free variants of Halley's method for multiple roots

机译：哈雷多重根算法的一些无二阶导数变体

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In this paper, we present two new families of third-order methods for finding multiple roots of nonlinear equations. Each of them is based on a variant of the Halley's method (for simple roots) free from second derivative. One of the families requires one evaluation of the function and two of its first derivative per iteration, and the other family requires two evaluations of the function and one of its first derivative. Several numerical examples are given to illustrate the performance of the presented methods.

机译：在本文中，我们介绍了两个新的三阶方法族，它们可以找到非线性方程的多个根。它们每个都是基于Halley方法的一种变体（对于简单根），不含二阶导数。一个族需要对函数进行一次评估，并且每次迭代需要对其一阶导数进行两次评估，而另一个族需要对函数进行一次评估，并且对其一阶导数进行一次评估。给出了几个数值示例来说明所提出方法的性能。

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《Applied mathematics and computation》 |2009年第6期|共7页
作者
Li SG; Li HS; Cheng LZ;
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原文格式 PDF
正文语种 eng
中图分类数值分析;
关键词
Halley's method; Multiple roots; Nonlinear equations; Iterative methods; Root finding;

机译：哈雷法;多重根;非线性方程;迭代法;求根;

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1. Some second-derivative-free variants of Halley's method for multiple roots [J] . Li SG, Li HS, Cheng LZ Applied mathematics and computation . 2009,第6期

机译：哈雷多重根算法的一些无二阶导数变体
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Some second-derivative-free variants of Halley's method for multiple roots

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