Computing parameter planes of iterative root-finding methods with several free critical points
Campos, Beatriz (Universitat Jaume I. Instituto Universitario de Matemáticas y Aplicaciones de Castellón)
Canela Sánchez, Jordi (Universitat Jaume I. Instituto Universitario de Matemáticas y Aplicaciones de Castellón)
Rodríguez-Arenas, Alberto (Universitat Politècnica de València)
Vindel, Pura (Universitat Jaume I. Instituto Universitario de Matemáticas y Aplicaciones de Castellón)

Date:	2025
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2020-118281GB-C32
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Root-finding algorithms ; Newton-like algorithms ; Parameter planes ; Several critical points
Published in:	Mathematics and computers in simulation, Vol. 228 (February 2025) , p. 52-72, ISSN 0378-4754

DOI: 10.1016/j.matcom.2024.08.013

21 p, 4.9 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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