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A multidimensional generalization of some classes of iterative methods

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Abstract

In this paper we extend to the multidimensional case some iterative methods that are known in their scalar version. All the schemes considered here are two-step methods with fourth-order local convergence, where the first step is Newton’s method. We analyze the efficiency of these new four algorithms and compare them in terms of the elapsed time needed for their computational implementation. We illustrate our results with some numerical examples and an application to the resolution of the systems arising from a Hammerstein’s integral equation.

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Authors and Affiliations

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

    Miquel Grau-Sánchez & Miquel Noguera

  2. Department of Mathematics and Computer Sciences, 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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Corresponding author

Correspondence to José M. Gutiérrez.

Additional information

This work was supported by the project MTM2014-52016-C2-1-P of the Spanish Ministry of Economy and Competitiveness.

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Grau-Sánchez, M., Noguera, M. & Gutiérrez, J.M. A multidimensional generalization of some classes of iterative methods. SeMA 74, 57–73 (2017). https://doi.org/10.1007/s40324-016-0080-2

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  • DOI: https://doi.org/10.1007/s40324-016-0080-2

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