Dynamics of the Secant map near infinity
IWe investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on (Formula presented.). We extend the Secant map to the real projective plane (Formula presented.). The line at infinity (Formula presented.) is in...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| 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:2072/531792 |
| Acceso en línea: | http://hdl.handle.net/2072/531792 |
| Access Level: | acceso abierto |
| Palabra clave: | Iteration Root finding algorithms Secant method |
| Sumario: | IWe investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on (Formula presented.). We extend the Secant map to the real projective plane (Formula presented.). The line at infinity (Formula presented.) is invariant, and there is one (if k is odd) or two (if k is even) fixed points at (Formula presented.). We show that these are of saddle type, and this allows us to better understand the dynamics of the Secant map near infinity. © 2022 Informa UK Limited, trading as Taylor & Francis Group. |
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