Frozen Iterative Methods Using Divided Differences “à la Schmidt–Schwetlick”

  • Miquel Grau-Sánchez
  • Miquel Noguera
  • José M. GutiérrezEmail author


The main goal of this paper is to study the order of convergence and the efficiency of four families of iterative methods using frozen divided differences. The first two families correspond to a generalization of the secant method and the implementation made by Schmidt and Schwetlick. The other two frozen schemes consist of a generalization of Kurchatov method and an improvement of this method applying the technique used by Schmidt and Schwetlick previously. An approximation of the local convergence order is generated by the examples, and it numerically confirms that the order of the methods is well deduced. Moreover, the computational efficiency indexes of the four algorithms are presented and computed in order to compare their efficiency.


Divided difference Order of convergence Nonlinear equations Iterative methods Efficiency 



The research of the three authors has been supported by a grant of the Spanish Ministry of Science and Innovation (Ref. MTM2011-28636-C02-01).


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Miquel Grau-Sánchez
    • 1
  • Miquel Noguera
    • 1
  • José M. Gutiérrez
    • 2
    Email author
  1. 1.Dept. of Applied Mathematics IITechnical University of CataloniaBarcelonaSpain
  2. 2.Dept. of Mathematics and ComputingUniversity of La RiojaLogroñoSpain

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