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On the efficiency of two variants of Kurchatov’s method for solving nonlinear systems

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Abstract

We consider Kurchatov’smethod and construct two variants of this method for solving systems of nonlinear equations and deduce their local R-orders of convergence in a direct symbolic computation. We also propose a generalization to several variables of the efficiency used in the scalar case and analyse the efficiencies of the three methods when they are used to solve systems of nonlinear equations.

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Acknowledgements

This research is supported by the National Center for Mathematics and Interdisciplinary Sciences, and by National Natural Science Foundation of China (Grant Nos. 60931002, 11001072 and 11101381), and partially by the Spanish Ministry of Science and Innovation under Grant AYA2009-14212-C05-05.

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Authors and Affiliations

  1. Department of Mathematics and Computation, University of La Rioja, 26004, Logroño, Spain

    José Antonio Ezquerro & Miguel Ángel Hernández

  2. Department of Applied Mathematics II, Technical University of Catalonia, 08034, Barcelona, Spain

    Angela Grau & Miquel Grau-Sánchez

Authors
  1. José Antonio Ezquerro
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  2. Angela Grau
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  3. Miquel Grau-Sánchez
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  4. Miguel Ángel Hernández
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Corresponding author

Correspondence to José Antonio Ezquerro.

Additional information

This work was supported in part by the project MTM2011-28636-C02-01 of the Spanish Ministry of Science and Innovation.

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Ezquerro, J.A., Grau, A., Grau-Sánchez, M. et al. On the efficiency of two variants of Kurchatov’s method for solving nonlinear systems. Numer Algor 64, 685–698 (2013). https://doi.org/10.1007/s11075-012-9685-4

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  • DOI: https://doi.org/10.1007/s11075-012-9685-4

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