Frozen Iterative Methods Using Divided Differences "à la Schmidt-Schwetlick"

  1. Grau-Sánchez, M. 1
  2. Noguera, M. 1
  3. Gutiérrez, J.M. 2
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Optimization Theory and Applications

ISSN: 0022-3239

Year of publication: 2014

Volume: 160

Issue: 3

Pages: 931-948

Type: Article

DOI: 10.1007/S10957-012-0216-1 SCOPUS: 2-s2.0-84896493624 WoS: WOS:000333339700012 GOOGLE SCHOLAR

More publications in: Journal of Optimization Theory and Applications

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Abstract

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. © 2012 Springer Science+Business Media New York.