Dynamics of Newton-like root finding methods
Campos, Beatriz (Universitat Jaume I. Instituto de Matemáticas y Aplicaciones de Castellón)
Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemátiques i Aplicacions de Castelló)
Vindel, Pura (Universitat Jaume I. Instituto de Matemáticas y Aplicaciones de Castellón)

Date:	2023
Abstract:	When exploring the literature, it can be observed that the operator obtained when applying Newton-like root finding algorithms to the quadratic polynomials z - c has the same form regardless of which algorithm has been used. In this paper, we justify why this expression is obtained. This is done by studying the symmetries of the operators obtained after applying Newton-like algorithms to a family of degree d polynomials p(z) = z - c. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algorithms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods.
Grants:	Agencia Estatal de Investigación PGC2018-095896-B-C22 Agencia Estatal de Investigación PID2020-118281GB-C32
Note:	Altres ajuts: project UJI-B2019-18
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Iterative methods ; Newton-like algorithms ; Complex dynamics of rational functions
Published in:	Numerical Algorithms, Vol. 93, Issue 4 (August 2023) , p. 1453-1480, ISSN 1572-9265

DOI: 10.1007/s11075-022-01474-w

28 p, 2.1 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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