Accessibility of Solutions by Newton's Method

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
International Journal of Computer Mathematics

ISSN: 0020-7160

Year of publication: 1995

Volume: 57

Issue: 3-4

Pages: 239-247

Type: Article

DOI: 10.1080/00207169508804427 SCOPUS: 2-s2.0-84954712005 WoS: WOS:A1995UH02600010 GOOGLE SCHOLAR

More publications in: International Journal of Computer Mathematics

Abstract

We give new conditions for the convergence of Newton's method in Banach spaces, in terms of the degree of logarithmic convexity. These conditions guarantee the convergence of Newton sequence in cases where the hypothesis of Kantorovich theorem are not verified, as we show in some examples