Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
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Títol
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomialsData de publicació
2020-03Editor
ElsevierISSN
1007-5704; 1878-7274Cita bibliogràfica
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. 105026Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://www.sciencedirect.com/science/article/pii/S1007570419303454Versió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
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 ... [+]
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. [-]
Publicat a
Communications in Nonlinear Science and Numerical Simulation, 2020, vol. 82Proyecto de investigación
Spanish project: MTM2014-52016-C02-2-P; Generalitat Valenciana: PROMETEO/2016/089; UJI project: P1.1B2015-16; French National Research Agency (ANR): ANR-13-BS01-0002Drets d'accés
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