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Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products

Author

Listed:
  • Alaa El Ichi

    (LABMIA-SI, Department of Mathematics, University Mohammed V Rabat, Rabat 10000, Morocco
    Department of Mathematics LMPA, 50 rue F. Buisson, ULCO, 62100 Calais, France)

  • Khalide Jbilou

    (Department of Mathematics LMPA, 50 rue F. Buisson, ULCO, 62100 Calais, France
    Laboratory of Modeling Simulation, Mohammed VI Polytechnic University, Hay Moulay Rachid, Ben Guerir 43150, Morocco)

  • Rachid Sadaka

    (LABMIA-SI, Department of Mathematics, University Mohammed V Rabat, Rabat 10000, Morocco)

Abstract

In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or ϵ -type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition.

Suggested Citation

  • Alaa El Ichi & Khalide Jbilou & Rachid Sadaka, 2020. "Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1298-:d:395074
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    References listed on IDEAS

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    1. Kuroda, Masahiro & Sakakihara, Michio, 2006. "Accelerating the convergence of the EM algorithm using the vector [epsilon] algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1549-1561, December.
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    Cited by:

    1. Oumaima Benchettou & Abdeslem Hafid Bentbib & Abderrahman Bouhamidi, 2023. "An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 111-134, July.
    2. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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