Numerical properties of different root-finding algorithms obtained for approximating continuous newton's method
This paper is dedicated to the study of continuous Newton's method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerica...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| 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/5bbc682bb750603269e803da |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc682bb750603269e803da |
| Access Level: | acceso abierto |
| Palabra clave: | Continuous newton's method Iterative methods Newton's method Nonlinear equations |
| Sumario: | This paper is dedicated to the study of continuous Newton's method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of convergence is particularly considered. We have analyzed both the cases of a constant and non-constant step size in the procedure of integration. We show that working with a non-constant step, the well-known Chebyshev-Halley family of iterative methods for solving nonlinear scalar equations is obtained. © 2015 by the authorlicensee MDPI, Basel, Switzerland. |
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