On the semilocal convergence of Newton–Kantorovich method under center-Lipschitz conditions

  1. Gutiérrez, J.M. 1
  2. Magreñán, Á.A. 1
  3. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2013

Volume: 221

Pages: 79-88

Type: Article

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DOI: 10.1016/J.AMC.2013.05.078 SCOPUS: 2-s2.0-84880349963 WoS: WOS:000324579400008 GOOGLE SCHOLAR

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Abstract

In this work we study Newton's method for solving nonlinear equations with operators defined between two Banach spaces. Together with the classical Kantorovich theory, we consider a center-Lipschitz condition for the Fréchet derivative of the involved operator. This fact allow us to obtain a majorizing sequence for the sequence defined in Banach spaces and to give conditions for the convergence. In this way, we obtain a generalization of Kantorovich's theorem that improves the values of the universal constant that appears in it as well as the radius where the solution is located and where it is unique. Finally we illustrate the main theoretical result by means of some examples. © 2013 Elsevier Inc. All rights reserved.