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Numerical Algorithms

, Volume 66, Issue 2, pp 241–267 | Cite as

An hybrid method that improves the accessibility of Steffensen’s method

  • J.A. EzquerroEmail author
  • M.A. Hernández-Verón
  • M.J. Rubio
  • A.I. Velasco
Original Paper

Abstract

Steffensen’s method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the accessibility of this method, we see that we can improve it by using the simplified secant method for predicting the initial approximation of Steffensen’s method. So, from both methods, we construct an hybrid iterative method which guarantees the convergence of Steffensen’s method from approximations given by the simplified secant method. We also emphasize that the study presented in this work is valid for equations with differentiable operators and non-differentiable operators.

Keywords

Nonlinear equation Non-differentiable operator Simplified secant method Steffensen’s method Hybrid method Semilocal convergence Domain of parameters 

Mathematics Subject Classification (2010)

47H99 65H10 65J15 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • J.A. Ezquerro
    • 1
    Email author
  • M.A. Hernández-Verón
    • 1
  • M.J. Rubio
    • 1
  • A.I. Velasco
    • 1
  1. 1.Department of Mathematics and ComputationUniversity of La RiojaLogroñoSpain

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