Dynamics of a family of Chebyshev-Halley type methods
In this paper, the dynamics of the Chebyshev-Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This set has interesting similarities with the Mandelbrot set. The parameter space has allowed us to find dif...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/54855 |
| Online Access: | https://riunet.upv.es/handle/10251/54855 |
| Access Level: | Open access |
| Keyword: | Nonlinear equations Iterative methods Dynamical behavior Quadratic polynomials Fatou and Julia sets Chebyshef-Halley method Non-convergence regions MATEMATICA APLICADA |
| Summary: | In this paper, the dynamics of the Chebyshev-Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This set has interesting similarities with the Mandelbrot set. The parameter space has allowed us to find different elements of the family which have bad convergence properties, since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method. (C) 2013 Elsevier Inc. All rights reserved. |
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