On the basins of attraction of a one-dimensional family of root finding algorithms
In this paper we study the dynamics of damped Traub's methods T when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which contain both Newton's (δ= 0) and Traub's method (δ= 1). Our goal is to obtain several topological properties...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:274783 |
| Acceso en línea: | https://ddd.uab.cat/record/274783 https://dx.doi.org/urn:doi:10.1007/s00209-023-03215-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Holomorphic dynamics Julia and Fatou sets Basins of attraction Root finding algorithms Simple connectivity Unboundedness |
| Sumario: | In this paper we study the dynamics of damped Traub's methods T when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which contain both Newton's (δ= 0) and Traub's method (δ= 1). Our goal is to obtain several topological properties of the basins of attraction of the roots of a polynomial p under T, which are used to determine a (universal) set of initial conditions for which convergence to all roots of p can be guaranteed. We also numerically explore the global properties of the dynamical plane for T to better understand the connection between Newton's method and Traub's method. |
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