How to solve nonlinear equations when a third order method is not applicable.

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
B I T-(Boletin Informativo de Telecomunicacion)

ISSN: 0210-3923

Year of publication: 1999

Volume: 39

Issue: 2

Pages: 255-269

Type: Article

SCOPUS: 2-s2.0-17144444621 WoS: WOS:000081188500004 GOOGLE SCHOLAR

More publications in: B I T-(Boletin Informativo de Telecomunicacion)

Institutional repository: lock_openOpen access Editor

Abstract

In this paper, we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. A Kantorovich-type convergence theorem is proved, so that the first Fréchet derivative of the operator satisfies a Lipschitz condition. We also give an explicit error bound.