Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations

  1. Ezquerro, J.A. 2
  2. Grau-Sánchez, M. 1
  3. Hernández, M.A. 2
  4. Noguera, M. 1
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year of publication: 2013

Volume: 398

Issue: 1

Pages: 100-112

Type: Article

DOI: 10.1016/J.JMAA.2012.08.040 SCOPUS: 2-s2.0-84867691493 WoS: WOS:000310659500009 GOOGLE SCHOLAR

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Abstract

From well-known secant-like methods, we observe that we can construct a new family of secant-like methods that includes the secant method and Kurchatov's method. We analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators. Finally, we apply our results to conservative problems. © 2012 Elsevier Ltd.