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An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems

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Abstract

Multipoint moment matching based methods are considered as powerful methods for model-order reduction problems. They are related to rational Krylov subspaces (classical or block ones) and are based on the selection of some interpolation points which is the major problem for these methods. In this work, an adaptive rational block Lanczos-type algorithm is proposed and applied for model order reduction of dynamical multi-input and multi-output linear time independent dynamical systems. We give some algebraic properties of the proposed algorithm and derive an explicit formulation of the error between the original and the reduced transfer functions. An adaptive method for choosing the interpolation points is also introduced. Finally, some numerical experiments are reported to show the effectiveness of the proposed adaptive rational block Lanczos-type process.

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Acknowledgments

We would like to thank the two referees for their helpful remarks and valuable suggestions. We also thank Serkan Gugercin for providing us with the matlab program of IRKA.

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Authors and Affiliations

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

    H. Barkouki & A. H. Bentbib

  2. Université du Littoral, Côte d’Opale, batiment H. Poincarré, 50 rue F. Buisson, 62280, Calais Cedex, France

    H. Barkouki & K. Jbilou

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  1. H. Barkouki
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  2. A. H. Bentbib
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  3. K. Jbilou
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Correspondence to K. Jbilou.

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Barkouki, H., Bentbib, A.H. & Jbilou, K. An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems. J Sci Comput 67, 221–236 (2016). https://doi.org/10.1007/s10915-015-0077-5

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