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Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

In this paper, we construct a family of iterative methods with memory from one without memory, analyzing their convergence and stability. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Some numerical tests confirm the theoretical results.

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References

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Acknowledgements

This research was partially supported by Ministerio de Economía y Competitividad under grants MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.

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Authors and Affiliations

  1. Instituto Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, València, Spain

    Alicia Cordero & Juan R. Torregrosa

  2. Facultat de Matemàtiques, Universitat de València, València, Spain

    Ivan Giménez

Authors
  1. Alicia Cordero
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  2. Ivan Giménez
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  3. Juan R. Torregrosa
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Corresponding author

Correspondence to Juan R. Torregrosa .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Cordero, A., Giménez, I., Torregrosa, J.R. (2019). Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_19

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

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