Enlarging The convergence domain of secant-like methods for equations

  1. Argyros, I.K. 1
  2. Ezquerro, J.A. 3
  3. Hernández-Verón, M.A. 3
  4. Hilout, S. 4
  5. Magreñán, Á.A. 2
  1. 1 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

  2. 2 Universidad Internacional de La Rioja
    info

    Universidad Internacional de La Rioja

    Logroño, España

    ROR https://ror.org/029gnnp81

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  4. 4 University of Poitiers
    info

    University of Poitiers

    Poitiers, Francia

    ROR https://ror.org/04xhy8q59

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Journal:
Taiwanese Journal of Mathematics

ISSN: 1027-5487

Year of publication: 2015

Volume: 19

Issue: 2

Pages: 629-652

Type: Article

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DOI: 10.11650/TJM.19.2015.4404 SCOPUS: 2-s2.0-84925358682 WoS: WOS:000351664500019 GOOGLE SCHOLAR

More publications in: Taiwanese Journal of Mathematics

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Abstract

We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton’s method and other popular methods as special cases. The convergence analysis is based on our idea of recurrent functions. Using more precise majorizing sequences than before we obtain weaker convergence criteria. These advantages are obtained because we use more precise estimates for the upper bounds on the norm of the inverse of the linear operators involved than in earlier studies. Numerical examples are given to illustrate the advantages of the new approaches. © 2015, Mathematical Society of the Rep. of China. All rights reserved.