Convergence of the relaxed Newton's method

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

Journal:
Journal of the Korean Mathematical Society

ISSN: 0304-9914

Year of publication: 2014

Volume: 51

Issue: 1

Pages: 137-162

Type: Article

DOI: 10.4134/JKMS.2014.51.1.137 SCOPUS: 2-s2.0-84891279431 WoS: WOS:000329769700009 GOOGLE SCHOLAR

More publications in: Journal of the Korean Mathematical Society

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Abstract

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < λ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter λ. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for λ = 1. © 2014 The Korean Mathematical Society.