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...

Descripción completa

Detalles Bibliográficos
Autores: Ezquerro, J.A. [0000-0001-8120-167X], Hernández, M.A. [0000-0001-5478-2958]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1998
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/5bbc69ebb750603269e823bc
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc69ebb750603269e823bc
Access Level:acceso abierto
Palabra clave:A priori error bounds
Convergence theorem
Nonlinear equations in Banach spaces
Recurrence relations
Third-order process
Two-point iteration
Descripción
Sumario: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.