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

Author

Listed:
  • Miquel Grau-Sánchez

    (Technical University of Catalonia)

  • Miquel Noguera

    (Technical University of Catalonia)

  • José M. Gutiérrez

    (University of La Rioja)

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.

Suggested Citation

  • Miquel Grau-Sánchez & Miquel Noguera & José M. Gutiérrez, 2014. "Frozen Iterative Methods Using Divided Differences “à la Schmidt–Schwetlick”," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 931-948, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-012-0216-1
    DOI: 10.1007/s10957-012-0216-1
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    References listed on IDEAS

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    1. J. A. Ezquerro & M. Grau-Sánchez & A. Grau & M. A. Hernández & M. Noguera & N. Romero, 2011. "On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 163-174, October.
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    Cited by:

    1. Amiri, Abdolreza & Argyros, Ioannis K., 2021. "On the approximation of mth power divided differences preserving the local order of convergence," Applied Mathematics and Computation, Elsevier, vol. 410(C).

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