Starting points for Newton's method under a center Lipschitz condition for the second derivative

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Internacional de La Rioja
    info

    Universidad Internacional de La Rioja

    Logroño, España

    ROR https://ror.org/029gnnp81

Revista:
Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Any de publicació: 2018

Volum: 330

Número: 1

Pàgines: 721-731

Tipus: Article

DOI: 10.1016/J.CAM.2016.12.013 SCOPUS: 2-s2.0-85009432127 WoS: WOS:000415783000051 GOOGLE SCHOLAR

Altres publicacions en: Journal of Computational and Applied Mathematics

Projectes relacionats

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

Resum

We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose to center the Lipschitz condition for the second derivative in a different point from that where Newton's method starts. This allows us to obtain different starting points for Newton's method and modify the domain of starting points. © 2016 Elsevier B.V.