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NUMERICAL SOLUTION OF LARGE-SCALE LYAPUNOV EQUATIONS AND MODEL REDUCTION PROBLEMS USING AN EXTENDED-RATIONAL BLOCK ARNOLDI METHOD

Abstract : In this paper, we propose a new block Krylov-type subspace method for model reduction in large scale dynamical systems. We also show how this method can be used to extract an approximate low rank solution of large-scale Lyapunov equations. We project the initial problem onto a new subspace, generated as combination of Rational and Polynomial block Krylov subspaces. Algebraic properties are given such as expressions of the error between the original and reduced transfer functions. Besides, a simplified expression of the residual, that allows us to compute the approximate solution in an efficient way, is established. Furthermore, we present an adaptive strategy of the interpolation points that will be used in the construction of our new block Krylov subspace. Numerical results are finally reported using some "benchmark examples" to confirm the performance of our method compared with other known methods.
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https://hal.archives-ouvertes.fr/hal-02568939
Contributor : Khalide Jbilou <>
Submitted on : Sunday, May 10, 2020 - 5:19:59 PM
Last modification on : Tuesday, January 5, 2021 - 5:24:02 PM

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O. Abidi, M. Hamadi, Khalide Jbilou, Y Kaouane, A. Ratnani. NUMERICAL SOLUTION OF LARGE-SCALE LYAPUNOV EQUATIONS AND MODEL REDUCTION PROBLEMS USING AN EXTENDED-RATIONAL BLOCK ARNOLDI METHOD. 2020. ⟨hal-02568939⟩

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