A general semilocal convergence result for Newton’s method under centered conditions for the second derivative

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Mathematical Modelling and Numerical Analysis

ISSN: 0764-583X

Year of publication: 2013

Volume: 47

Issue: 1

Pages: 149-167

Type: Article

DOI: 10.1051/M2AN/2012026 SCOPUS: 2-s2.0-84996129118 WoS: WOS:000313646300007 GOOGLE SCHOLAR

More publications in: Mathematical Modelling and Numerical Analysis

Abstract

From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type