Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
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 guara...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:228105 |
| Acesso em linha: | https://ddd.uab.cat/record/228105 https://dx.doi.org/urn:doi:10.1016/j.cnsns.2019.105026 |
| Access Level: | acceso abierto |
| Palavra-chave: | Iterative methods Complex dynamics of rational functions Chebyshev-Halley family Parameter plane |
| Resumo: | 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 zⁿ +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. |
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