<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Initial conditions can have a substantial impact on the behavior of iterative root-finding techniques for nonlinear equations. By allowing complex starting points and complex roots, it is possible to examine the basins of attraction in the complex plane in order to compare the performance of various iterative techniques. In this paper, a one-parameter family of third-order root-finding methods is studied by varying its parameter <italic>A</italic> within −2.0 and 2.4 and applying it to a polynomial equation of high degree (degree 25). This family includes the Euler–Chebyshev’s (<italic>A</italic> = 0), Halley’s (<italic>A</italic> = 1) and BSC (<italic>A</italic> = 2) techniques. According to the results, the one-parameter family provides the best performance for values near <italic>A</italic> = 1, which equals to the Halley’s method.</p>
</abstract>

Initial conditions can have a substantial impact on the behavior of iterative root-finding techniques for nonlinear equations. By allowing complex starting points and complex roots, it is possible to examine the basins of attraction in the complex plane in order to compare the performance of various iterative techniques. In this paper, a one-parameter family of third-order root-finding methods is studied by varying its parameter A within −2.0 and 2.4 and applying it to a polynomial equation of high degree (degree 25). This family includes the Euler–Chebyshev’s (A = 0), Halley’s (A = 1) and BSC (A = 2) techniques. According to the results, the one-parameter family provides the best performance for values near A = 1, which equals to the Halley’s method.

Basins of attraction of a one-parameter family of root-finding techniques

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Basins of attraction of a one-parameter family of root-finding techniques"}

Initial conditions can have a substantial impact on the behavior of iterative root-finding techniques for nonlinear equations. By allowing complex starting...

单参数根寻技术家族的吸引力基础

在线发布:2023年9月29日

页面范围： 354 - 364

收到:2022年12月10日

认可的:2023年9月7日

内政部： https://doi.org/10.2478/mjpaa-2023-0024

关键词
多项式方程,非线性方程,迭代寻根方法,收敛顺序,吸引力的基础

©2023 Mário Basto等人，由Sciendo出版

本作品根据知识共享署名-非商业性-非衍生产品4.0国际许可证授权。