On the basins of attraction of a one-dimensional family of root finding algorithms : from Newton to Traub
Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemátiques i Aplicacions de Castelló)
Evdoridou, Vasiliki (The Open University. School of Mathematics and Statistics (UK))
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)

Date:	2023
Abstract:	In this paper we study the dynamics of damped Traub's methods T when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which contain both Newton's (δ= 0) and Traub's method (δ= 1). Our goal is to obtain several topological properties of the basins of attraction of the roots of a polynomial p under T, which are used to determine a (universal) set of initial conditions for which convergence to all roots of p can be guaranteed. We also numerically explore the global properties of the dynamical plane for T to better understand the connection between Newton's method and Traub's method.
Grants:	Ministerio de Economía y Competitividad MDM-2014-0445 Agencia Estatal de Investigación PID2020-118281GB-C33 Agencia Estatal de Investigación PID2020-118281GB-C32
Note:	Altres ajuts: BGSMath Banco de Santander Postdoctoral 2017; the project UJI-B2019-18 from Universitat Jaume I; IMUB
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:	Holomorphic dynamics ; Julia and Fatou sets ; Basins of attraction ; Root finding algorithms ; Simple connectivity ; Unboundedness
Published in:	Mathematische Zeitschrift, Vol. 303, Issue 3 (March 2023) , art. 55, ISSN 1432-1823

DOI: 10.1007/s00209-023-03215-8

22 p, 2.1 MB

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