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

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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.

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Acknowledgements

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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Authors and Affiliations

  1. Dept. of Applied Mathematics II, Technical University of Catalonia, Jordi Girona 1-3, 08034, Barcelona, Spain

    Miquel Grau-Sánchez & Miquel Noguera

  2. Dept. of Mathematics and Computing, University of La Rioja, Luis de Ulloa s/n, 26004, Logroño, Spain

    José M. Gutiérrez

Authors
  1. Miquel Grau-Sánchez
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  2. Miquel Noguera
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  3. José M. Gutiérrez
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Correspondence to José M. Gutiérrez.

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Grau-Sánchez, M., Noguera, M. & Gutiérrez, J.M. Frozen Iterative Methods Using Divided Differences “à la Schmidt–Schwetlick”. J Optim Theory Appl 160, 931–948 (2014). https://doi.org/10.1007/s10957-012-0216-1

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  • DOI: https://doi.org/10.1007/s10957-012-0216-1

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