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Algorithm of Competing Processes for the Richardson Iteration Method with the Chebyshev Parameters

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Numerical Analysis and Its Applications (NAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

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Abstract

A method for solving linear systems of equations with sign-definite self-adjoint operator matrix by the Richardson iteration method in case of the absence of information about the lower spectral bound of a problem is presented. The algorithm is based on the simultaneous operation of two competing iterative processes, the effectiveness of which is constantly analyzed. The method is explained on an example of one-dimensional steady-state heat equation.

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References

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Acknowledgements

This project has received funding from Russian Science Foundation (project no. 16-11-00100).

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Authors and Affiliations

  1. Univ. Lyon, ENS de Lyon, Univ. Lyon1, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, 69007, Lyon, France

    Mikhail V. Popov

  2. Keldysh Institute of Applied Mathematics, 4 Miusskaya sq., 125047, Moscow, Russia

    Mikhail V. Popov, Yuriy A. Poveschenko, Igor V. Popov & Vladimir A. Gasilov

  3. National Research Nuclear University MEPhI, 31 Kashirskoe sh., 115409, Moscow, Russia

    Yuriy A. Poveschenko, Igor V. Popov & Vladimir A. Gasilov

  4. Moscow Institute of Physics and Technology, Dolgoprudnyy, 141700, Moscow Region, Russia

    Alexander V. Koldoba

Authors
  1. Mikhail V. Popov
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  2. Yuriy A. Poveschenko
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  3. Igor V. Popov
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  4. Vladimir A. Gasilov
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  5. Alexander V. Koldoba
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Corresponding author

Correspondence to Mikhail V. Popov .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Popov, M.V., Poveschenko, Y.A., Popov, I.V., Gasilov, V.A., Koldoba, A.V. (2017). Algorithm of Competing Processes for the Richardson Iteration Method with the Chebyshev Parameters. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_64

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_64

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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