Avoiding the computation of the second Fréchet-derivative in the Convex Acceleration of Newton's method.
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Universidad de La Rioja
info
ISSN: 0377-0427
Año de publicación: 1998
Volumen: 96
Número: 1
Páginas: 1-12
Tipo: Artículo
Otras publicaciones en: Journal of Computational and Applied Mathematics
Resumen
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.