Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can...
| Autores: | , , |
|---|---|
| Tipo de recurso: | capítulo de libro |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc67f2b750603269e800c4 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc67f2b750603269e800c4 |
| Access Level: | acceso abierto |
| Palabra clave: | box-counting Chebyshev-Halley methods fractal dimension Julia set |
| Sumario: | The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can define the universal fractal dimension of the aforementioned algorithms as the fractal dimension of they corresponding universal Julia sets. © 2011 American Institute of Physics. |
|---|