A modification of the classic conditions of Newton-Kantorovich for Newton's method

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Mathematical and Computer Modelling

ISSN: 0895-7177

Año de publicación: 2012

Volumen: 57

Número: 3-4

Páginas: 584-594

Tipo: Artículo

DOI: 10.1016/J.MCM.2012.07.015 SCOPUS: 2-s2.0-84870537821 WoS: WOS:000311911700025 GOOGLE SCHOLAR

Otras publicaciones en: Mathematical and Computer Modelling

Resumen

We study the semilocal convergence of Newton's method in Banach spaces under a modification of the classic conditions of Kantorovich, which leads to a generalization of Kantorovich's theory. We illustrate this study with two Hammerstein integral equations of the second kind, where the classic conditions of Kantorovich cannot be applied, but our modification of them can. © 2012 Elsevier Ltd.