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Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side

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Abstract

Motivated by the effectiveness of Krylov projection methods and the CP decomposition of tensors, which is a low rank decomposition, we propose Arnoldi-based methods (block and global) to solve Sylvester tensor equation with low rank right-hand sides. We apply a standard Krylov subspace method to each coefficient matrix, in order to reduce the main problem to a projected Sylvester tensor equation, which can be solved by a global iterative scheme. We show how to extract approximate solutions via matrix Krylov subspaces basis. Several theoretical results such as expressions of residual and its norm are presented. To show the performance of the proposed approaches, some numerical experiments are given.

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Authors and Affiliations

  1. Laboratory LAMAI, University Cadi Ayyad, Marrakesh, Morocco

    A. H. Bentbib & S. El-Halouy

  2. Laboratory LabSIPE, ENSA, d’El Jadida, University Chouaib Doukkali, El Jadida, Morocco

    El M. Sadek

Authors
  1. A. H. Bentbib
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  2. S. El-Halouy
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  3. El M. Sadek
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Correspondence to S. El-Halouy.

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Bentbib, A.H., El-Halouy, S. & Sadek, E.M. Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side. Numer Algor 84, 1411–1430 (2020). https://doi.org/10.1007/s11075-020-00874-0

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