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On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
dc.contributor.author | Canela, Jordi | |
dc.contributor.author | Evdoridou, Vasiliki | |
dc.contributor.author | Garijo, Antonio | |
dc.contributor.author | Jarque, Xavier | |
dc.date.accessioned | 2023-03-07T08:34:54Z | |
dc.date.available | 2023-03-07T08:34:54Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | CANELA, Jordi, et al. On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub. Mathematische Zeitschrift, 2023, vol. 303, no 3, p. 55. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/201948 | |
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. | ca_CA |
dc.description.sponsorShip | Funding for open access charge: CRUE-Universitat Jaume I | |
dc.format.extent | 22 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Springer | ca_CA |
dc.relation.isPartOf | Mathematische Zeitschrift, 303, 55 (2023) | ca_CA |
dc.rights | © The Author(s) 2023, corrected publication 2023 | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | ca_CA |
dc.subject | Holomorphic dynamics | ca_CA |
dc.subject | Julia and Fatou sets | ca_CA |
dc.subject | Basins of attraction | ca_CA |
dc.subject | Root finding algorithms | ca_CA |
dc.subject | Simple connectivity | ca_CA |
dc.subject | Unboundedness | ca_CA |
dc.title | On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1007/s00209-023-03215-8 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://link.springer.com/article/10.1007/s00209-023-03215-8 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Universitat Jaume I | ca_CA |
project.funder.name | CRUE-CSIC agreement with Springer Nature | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad | ca_CA |
project.funder.name | BGSMath Banco de Santander Postdoctoral 2017 | ca_CA |
project.funder.name | London Mathematical Society | ca_CA |
project.funder.name | IMUB | ca_CA |
project.funder.name | EPSRC | ca_CA |
oaire.awardNumber | PID2020-118281GB-C32 | ca_CA |
oaire.awardNumber | PID2020-118281GB-C33 | ca_CA |
oaire.awardNumber | EP/R010560/1 | ca_CA |
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