Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains

  1. I. K. Argyros 2
  2. J.A. Ezquerro 1
  3. M.A. Hernández-Verón 1
  4. A. A. Magreñán 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

Proceedings:
Proceedings of the 16th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016, Costa Ballena (Rota), Cádiz, Spain July 4th -8th , 2016

Publisher: CMMSE

ISBN: 978-84-608-6082-2

Year of publication: 2016

Pages: 114-117

Congress: 16th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE 2016 (16º. 2016. Rota, Cádiz)

Type: Conference paper

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Abstract

We present new sufficient convergence conditions for the semilocal convergence ofNewton’s method to a locally unique solution of a nonlinear equation in a Banach space.We use H¨older and center H¨older conditions, instead of just H¨older conditions, for thefirst derivative of the operator involved in the convergence study. The new convergenceconditions are weaker than others required in earlier studies.