计算具有多个自由临界点的迭代寻根方法的参数平面

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-09-03 DOI:10.1016/j.matcom.2024.08.013

Beatriz Campos , Jordi Canela , Alberto Rodríguez-Arenas , Pura Vindel

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引用次数: 0

摘要

本文提出了一种算法，用于获取具有多个自由临界点的寻根方法族的参数平面。参数平面显示了所有临界点的共同行为。我们通过绘制具有两个和三个临界点的不同牛顿样方法的参数平面，分析了该算法的适用性。我们还介绍了牛顿类算子及其导数用宫格多项式表达的一些结果，并展示了如何获得具有实系数的牛顿类方法的临界点表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computing parameter planes of iterative root-finding methods with several free critical points

In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the inconsistencies arising from the relationship between the different critical points as well as the indeterminacy caused by the square roots involved in their computation.

We analyse the suitability of this algorithm by drawing the parameter planes of different Newton-like methods with two and three critical points. We also present some results of the expressions of the Newton-like operators and their derivatives in terms of palindromic polynomials, and we show how to obtain the expression of the critical points of a Newton-like method with real coefficients.

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.