Enlarging the domain of starting points for Newton's method under center conditions on the first Fréchet-derivative

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revue:
Journal of Complexity

ISSN: 0885-064X

Année de publication: 2016

Volumen: 33

Pages: 89-106

Type: Article

DOI: 10.1016/J.JCO.2015.09.007 SCOPUS: 2-s2.0-84959356150 WoS: WOS:000370090400005 GOOGLE SCHOLAR

D'autres publications dans: Journal of Complexity

Projets liés

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Résumé

We analyze the semilocal convergence of Newton's method under center conditions on the first Fréchet-derivative of the operator involved. We see that we can extend the known results so far, since we provide different starting points from the point where the first Fréchet-derivative is centered (that is the situation usually considered by other authors), so that the domain of starting points is enlarged for Newton's method. We also illustrate the theoretical results obtained with some mildly nonlinear elliptic equations. © 2015 Elsevier Inc. All rights reserved.