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

Journal:
Mathematical and Computer Modelling

ISSN: 0895-7177

Year of publication: 2012

Volume: 57

Issue: 3-4

Pages: 584-594

Type: Article

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

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Abstract

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.