Generalized Differentiability Conditions for Newton's Method.

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revue:
IMA journal of numerical analysis

ISSN: 0272-4979

Année de publication: 2002

Volumen: 22

Número: 2

Pages: 187-205

Type: Article

DOI: 10.1093/IMANUM/22.2.187 SCOPUS: 2-s2.0-0345016431 WoS: WOS:000174797200002 GOOGLE SCHOLAR

D'autres publications dans: IMA journal of numerical analysis

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Résumé

The use of majorizing sequences is the usual way to prove the convergence of Newton's method. An alternative technique to majorizing sequences is provided in this paper, in which three scalar sequences are used, so that the analysis of convergence is simplified when the traditional convergence condition is relaxed. An application to a nonlinear integral equation is also given, which is also solved and the solution approximated by a discretization process.