How to Improve the Domain of Starting Points for 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:
Studies in Applied Mathematics

ISSN: 0022-2526

Year of publication: 2014

Volume: 132

Issue: 4

Pages: 354-380

Type: Article

DOI: 10.1111/SAPM.12033 SCOPUS: 2-s2.0-84898852888 WoS: WOS:000334290200003 GOOGLE SCHOLAR

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Abstract

We analyze the semilocal convergence of Steffensen's method, using a novel technique, which is based on recurrence relations, for solving systems of nonlinear equations. This technique allows analyzing the convergence of Steffensen's method to solutions of equations, where the function involved can be both differentiable and nondifferentiable. Moreover, this technique also allows enlarging the domain of starting points for Steffensen's method from certain predictions with the simplified Steffensen method. © 2013 by the Massachusetts Institute of Technology.