Convergence regions for the Chebyshev-Halley family
In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree $n$ polynomials $z^{n}+c$. We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having $z=\in...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/159358 |
| Acceso en línea: | https://hdl.handle.net/2445/159358 |
| Access Level: | acceso abierto |
| Palabra clave: | Sistemes de Chebyshev Polinomis Chebyshev systems Polynomials |
| Sumario: | In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree $n$ polynomials $z^{n}+c$. We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having $z=\infty $ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of $n$ grows. We also demonstrate that, although the convergence order of the Chebyshev-Halley family is 3, there is a member of order 4 for each value of $n$. In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots. |
|---|