Increasing the applicability of Steffensen's method

  1. Ezquerro, J.A. 1
  2. Hernández-Verón, M.A. 1
  1. 1 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: 2014

Volume: 418

Issue: 2

Pages: 1062-1073

Type: Article

DOI: 10.1016/J.JMAA.2014.04.042 SCOPUS: 2-s2.0-84900541958 WoS: WOS:000336887700031 GOOGLE SCHOLAR

More publications in: Journal of Mathematical Analysis and Applications

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Abstract

We present an original alternative to the majorant principle of Kantorovich to study the semilocal convergence of Steffensen's method when it is applied to solve nonlinear systems which are differentiable. This alternative allows choosing starting points from which the convergence of Steffensen's method is guaranteed, but it is not from the majorant principle. Moreover, this study extends the applicability of Steffensen's method to the solution of nonlinear systems which are nondifferentiable and improves a previous result given by the authors. © 2014 Elsevier Inc. All rights reserved.