dc.contributor.author
Canela, J.
dc.contributor.author
Evdoridou, V.
dc.contributor.author
Garijo, A.
dc.contributor.author
Jarque, X.
dc.date.accessioned
2023-06-21T13:34:58Z
dc.date.accessioned
2024-09-19T14:25:24Z
dc.date.available
2023-06-21T13:34:58Z
dc.date.available
2024-09-19T14:25:24Z
dc.date.issued
2023-02-04
dc.identifier.uri
http://hdl.handle.net/2072/535458
dc.description.abstract
In this paper we study the dynamics of damped Traub’s methods Tδ 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 T1, 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 Tδ to better understand the connection between Newton’s method and Traub’s method. © 2023, The Author(s).
eng
dc.description.sponsorship
Engineering and Physical Sciences Research Council, EPSRC: EP/R010560/1, PID2020-118281GB-C32; London Mathematical Society, LMS; Ministerio de Economía y Competitividad, MINECO: MDM-2014-0445, UJI-B2019-18; Universitat Jaume I, UJI; Universitat de Barcelona, UB. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first author was supported by the Spanish Ministry of Economy and Competitiveness through the María de Maeztu Programme for Units of Excellence in R &D (MDM-2014-0445), by BGSMath Banco de Santander Postdoctoral 2017, and by the project UJI-B2019-18 from Universitat Jaume I. The second author was supported by the London Mathematical Society, the IMUB and the EPSRC grant EP/R010560/1. The third author was supported by PID2020-118281GB-C33. The first and fourth authors were supported by PID2020-118281GB-C32. We are grateful to the anonymous referee for all his/her suggestions which have clearly improved the previous version of this paper. We also thank the Institute of Mathematics at Universitat de Barcelona (IMUB) for the hospitality during the visit of the second author, when this project started.This work also acknowledges the CERCA Programme of the Generalitat de Catalunya for institutional support. This work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M).
dc.publisher
Springer Science and Business Media Deutschland GmbH
dc.relation.ispartof
Mathematische Zeitschrift
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Basins of attraction; Holomorphic dynamics; Julia and Fatou sets; Root finding algorithms; Simple connectivity; Unboundedness
dc.title
On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
dc.type
info:eu-repo/semantics/article
dc.type
info:eu-repo/semantics/publishedVersion
dc.identifier.doi
10.1007/s00209-023-03215-8
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
