On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
In this paper we study the dynamics of damped Traub’s methods Tδ 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 a...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/535458 |
| Acceso en línea: | http://hdl.handle.net/2072/535458 |
| Access Level: | acceso abierto |
| Palabra clave: | Basins of attraction Holomorphic dynamics Julia and Fatou sets Root finding algorithms Simple connectivity Unboundedness |
| Sumario: | In this paper we study the dynamics of damped Traub’s methods Tδ 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 T1, 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 Tδ to better understand the connection between Newton’s method and Traub’s method. © 2023, The Author(s). |
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