A Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods

  1. Argyros, I.K. 1
  2. González, D. 2
  3. Magreñán, Á.A. 2
  1. 1 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Function Spaces

ISSN: 2314-8896

Year of publication: 2014

Pages: 1-11

Type: Article

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DOI: 10.1155/2014/467980 SCOPUS: 2-s2.0-84899441911 WoS: WOS:000332296400001 GOOGLE SCHOLAR

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Abstract

We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methods (including the secant and Kurchatov method as special cases) in a Banach space setting (Ezquerro et al., 2000-2012). Using our idea of recurrent functions and tighter majorizing sequences, we provide convergence results under the same or less computational cost than the ones of Ezquerro et al., (2013, 2010, and 2012) and Hernandez et al., (2000, 2005, and 2002) and with the following advantages: weaker sufficient convergence conditions, tighter error estimates on the distances involved, and at least as precise information on the location of the solution. Numerical examples validating our theoretical results are also provided in this study.