Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
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comunitat-uji-handle2:10234/173364
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Title
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomialsDate
2020-03Publisher
ElsevierISSN
1007-5704; 1878-7274Bibliographic 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. 105026Type
info:eu-repo/semantics/articlePublisher version
https://www.sciencedirect.com/science/article/pii/S1007570419303454Version
info:eu-repo/semantics/submittedVersionSubject
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 ... [+]
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. [-]
Is part of
Communications in Nonlinear Science and Numerical Simulation, 2020, vol. 82Investigation project
Spanish project: MTM2014-52016-C02-2-P; Generalitat Valenciana: PROMETEO/2016/089; UJI project: P1.1B2015-16; French National Research Agency (ANR): ANR-13-BS01-0002Rights
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