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A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method

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Abstract

In this paper, we propose a new block Krylov-type subspace method for model reduction in large scale dynamical systems. We project the initial problem onto a new subspace, generated as a combination of rational and polynomial block Krylov subspaces. Simple algebraic properties are given and expressions of the error between the original and reduced transfer functions are established. Furthermore, we present an adaptive strategy of the interpolation points that will be used in the construction of our new block Krylov subspace. We also show how this method can be used to extract an approximate low rank solution of large-scale Lyapunov equations. Numerical results are reported on some benchmark examples to confirm the performance of our method compared with other known methods.

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Notes

  1. http://slicot.org/20-site/126-benchmark-examples-for-model-reduction.

  2. https://www.mathworks.com/matlabcentral/fileexchange/59169-sssmor-toolbox.

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Acknowledgements

The authors wish to express their appreciations to the Reviewers for their insightful comments and suggestions that lead to an improved paper.

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Authors and Affiliations

  1. Laboratory of Modeling Simulation and Data Analysis, Mohammed VI Polytechnic University, Hay Moulay Rachid, 43150, Ben Guerir, Morocco

    M. A. Hamadi, K. Jbilou & A. Ratnani

  2. Department of Mathematics LMPA, ULCO, 50 rue F. Buisson, Calais, 62100, France

    M. A. Hamadi & K. Jbilou

Authors
  1. M. A. Hamadi
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  2. K. Jbilou
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  3. A. Ratnani
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Correspondence to M. A. Hamadi.

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Hamadi, M.A., Jbilou, K. & Ratnani, A. A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method. J. Appl. Math. Comput. 68, 271–293 (2022). https://doi.org/10.1007/s12190-021-01521-0

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