A new semilocal convergence theorem for Newton's method

  1. Gutiérrez, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Año de publicación: 1997

Volumen: 79

Número: 1

Páginas: 131-145

Tipo: Artículo

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DOI: 10.1016/S0377-0427(97)81611-1 SCOPUS: 2-s2.0-0031550718 WoS: WOS:A1997WN38700009 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Computational and Applied Mathematics

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x)=0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition. Results on uniqueness of solution and error estimates are also given. Finally, these results are compared with those that use Kantorovich conditions.