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Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations

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Abstract

In this paper, we present a new numerical methods for solving large-scale differential Sylvester matrix equations with low rank right hand sides. These differential matrix equations appear in many applications such as robust control problems, model reduction problems and others. We present two approaches based on extended global Arnoldi process. The first one is based on approximating exponential matrix in the exact solution using the global extended Krylov method. The second one is based on a low-rank approximation of the solution of the corresponding Sylvester equation using the extended global Arnoldi algorithm. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed methods compared with the extended block Krylov method given in Hached and Jbilou (Numer Linear Algebra Appl 255:e2187, 2018).

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Authors and Affiliations

  1. Laboratory of Engineering Sciences for Energy, National School of Applied Sciences of El Jadida, University Chouaib Doukkali, El Jadida, Morocco

    El. Mostafa Sadek

  2. Faculté des Sciences et Techniques-Gueliz, Laboratoire de Mathématiques Appliquées et Informatique, Marrakech, Morocco

    Abdeslem Hafid Bentbib

  3. Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Morocco

    Lakhlifa Sadek & Hamad Talibi Alaoui

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  1. El. Mostafa Sadek
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  2. Abdeslem Hafid Bentbib
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  3. Lakhlifa Sadek
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  4. Hamad Talibi Alaoui
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Correspondence to El. Mostafa Sadek.

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Sadek, E.M., Bentbib, A.H., Sadek, L. et al. Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations. J. Appl. Math. Comput. 62, 157–177 (2020). https://doi.org/10.1007/s12190-019-01278-7

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  • DOI: https://doi.org/10.1007/s12190-019-01278-7

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