Avoiding the computation of the second Fréchet-derivative in the Convex Acceleration of Newton's method.

  1. Ezquerro, J.A. 1
  2. Hernández, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Any de publicació: 1998

Volum: 96

Número: 1

Pàgines: 1-12

Tipus: Article

SCOPUS: 2-s2.0-0040964586 WoS: WOS:000075896200001 DIALNET GOOGLE SCHOLAR

Altres publicacions en: Journal of Computational and Applied Mathematics

Repositori institucional: lock_openAccés obert Editor

Resum

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.