The Secant Method and Divided Differences Hölder Continuous.
We apply the Secant method to solve non-linear operator equations in Banach spaces. A semilocal convergence result is obtained, where the first-order divided difference of the non-linear operator is Hölder continuous. For that, we use a technique based on a new system of recurrence relations to obta...
| Autores: | , |
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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/5bbc69f3b750603269e82449 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc69f3b750603269e82449 |
| Access Level: | acceso abierto |
| Palabra clave: | A priori error bounds Boundary value problems Recurrence relations The secant method |
| Sumario: | We apply the Secant method to solve non-linear operator equations in Banach spaces. A semilocal convergence result is obtained, where the first-order divided difference of the non-linear operator is Hölder continuous. For that, we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution and give an explicit expression for the a priori error bounds. Moreover, we apply our results to the numerical solution of a non-linear boundary value problem of second-order. © 2001 Elsevier Science Inc. All rights reserved. |
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