An hybrid method that improves the accessibility of Steffensen's method
Steffensen's method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the accessibility of this method, we see that we can improve it by using the simplified secant method for predicting the initial approximation of Steffensen�...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| 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/5bbc69b1b750603269e81fcc |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc69b1b750603269e81fcc |
| Access Level: | acceso abierto |
| Palabra clave: | Domain of parameters Hybrid method Non-differentiable operator Nonlinear equation Semilocal convergence Simplified secant method Steffensen's method |
| Sumario: | Steffensen's method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the accessibility of this method, we see that we can improve it by using the simplified secant method for predicting the initial approximation of Steffensen's method. So, from both methods, we construct an hybrid iterative method which guarantees the convergence of Steffensen's method from approximations given by the simplified secant method. We also emphasize that the study presented in this work is valid for equations with differentiable operators and non-differentiable operators. © 2013 Springer Science+Business Media New York. |
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