Avoiding the computation of the second Fréchet-derivative in the Convex Acceleration of Newton's method.
We introduce a new two-step method to approximate a solution of a nonlinear operator equation in a Banach space. An existence-uniqueness theorem and error estimates are provided for this iteration using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1998 |
| País: | España |
| Recursos: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc69ebb750603269e823bc |
| Acesso em linha: | https://investigacion.unirioja.es/documentos/5bbc69ebb750603269e823bc |
| Access Level: | acceso abierto |
| Palavra-chave: | A priori error bounds Convergence theorem Nonlinear equations in Banach spaces Recurrence relations Third-order process Two-point iteration |
| Resumo: | We introduce a new two-step method to approximate a solution of a nonlinear operator equation in a Banach space. An existence-uniqueness theorem and error estimates are provided for this iteration using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. For a special choice of the parameter involved we use, our method is of fourth order. © 1998 Elsevier Science B.V. All rights reserved. |
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