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Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
dc.contributor.author | Campos, Beatriz | |
dc.contributor.author | Canela, Jordi | |
dc.contributor.author | Vindel, Pura | |
dc.date.accessioned | 2020-03-10T08:05:22Z | |
dc.date.available | 2020-03-10T08:05:22Z | |
dc.date.issued | 2020-03 | |
dc.identifier.citation | CAMPOS, Beatriz; CANELA, Jordi; VINDEL, Purificación. Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials. Communications in Nonlinear Science and Numerical Simulation, 2020, vol. 82, p. 105026 | ca_CA |
dc.identifier.issn | 1007-5704 | |
dc.identifier.issn | 1878-7274 | |
dc.identifier.uri | http://hdl.handle.net/10234/186938 | |
dc.description.abstract | We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the roots may be slower when the basins of attraction are not simply connected. In this paper we provide a criterion which guarantees the simple connectivity of the basins of attraction of the roots. We use the criterion for the Chebyshev-Halley methods applied to the degree n polynomials z n + c, obtaining a characterization of the parameters for which all Fatou components are simply connected and, therefore, the Julia set is connected. We also study how increasing n affects the dynamics. | ca_CA |
dc.format.extent | 19 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.relation.isPartOf | Communications in Nonlinear Science and Numerical Simulation, 2020, vol. 82 | ca_CA |
dc.rights | Copyright © Elsevier | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | iterative methods | ca_CA |
dc.subject | complex dynamics of rational functions | ca_CA |
dc.subject | Chebyshev-Halley family | ca_CA |
dc.subject | parameter plane | ca_CA |
dc.title | Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.cnsns.2019.105026 | |
dc.relation.projectID | Spanish project: MTM2014-52016-C02-2-P; Generalitat Valenciana: PROMETEO/2016/089; UJI project: P1.1B2015-16; French National Research Agency (ANR): ANR-13-BS01-0002 | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://www.sciencedirect.com/science/article/pii/S1007570419303454 | ca_CA |
dc.type.version | info:eu-repo/semantics/submittedVersion | ca_CA |
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