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A family of iterative methods that uses divided differences of first and second orders

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Abstract

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592–9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.

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Authors and Affiliations

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

    J. A. Ezquerro & M. A. Hernández-Verón

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

    M. Grau-Sánchez & M. Noguera

Authors
  1. J. A. Ezquerro
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  2. M. Grau-Sánchez
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  3. M. A. Hernández-Verón
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  4. M. Noguera
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Corresponding author

Correspondence to J. A. 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-Sánchez, M., Hernández-Verón, M.A. et al. A family of iterative methods that uses divided differences of first and second orders. Numer Algor 70, 571–589 (2015). https://doi.org/10.1007/s11075-015-9962-0

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  • DOI: https://doi.org/10.1007/s11075-015-9962-0

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