The Newton's method for operators with Hölder continuous ffrst derivative.
We analyze the convergence of the Newton method when the first Fréchet derivative of the operator involved is Hölder continuous. We calculate also the R-order of convergence and provide some a priori error bounds. Based on this study, we give some results on the existence and uniqueness of the solut...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2001 |
| 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/5bbc69f2b750603269e8243f |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc69f2b750603269e8243f |
| Access Level: | acceso abierto |
| Palabra clave: | A priori error bounds Hammerstein integral equation Newton method Nonlinear equations in Banach spaces Recurrence relations Semilocal convergence theorem |
| Sumario: | We analyze the convergence of the Newton method when the first Fréchet derivative of the operator involved is Hölder continuous. We calculate also the R-order of convergence and provide some a priori error bounds. Based on this study, we give some results on the existence and uniqueness of the solution for a nonlinear Hammerstein integral equation of the second kind. |
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