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A Computational Method for Symmetric Stein Matrix Equations

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Numerical Linear Algebra in Signals, Systems and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 80))

Abstract

In the present paper, we propose a numerical method for solving the sparse symmetric Stein equation \(AXA^T-X+BB^T=0.\) Such problems appear in control problems, filtering and image restoration. The proposed method is a Krylov subspace method based on the global Arnoldi algorithm. We apply the global Arnoldi algorithm to extract low-rank approximate solutions to Stein matrix equations. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.

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Acknowledgements

We would like to thank the referees for helpful remarks and useful suggestions.

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Authors and Affiliations

  1. Université du Littoral, zone universitaire de la Mi-voix, batiment H. Poincarré, 50 rue F. Buisson, B.P. 699, 62280, Calais Cedex, France

    K. Jbilou

  2. Département d’Informatique, Ecole Normale Supérieure Takaddoum, Av. Oued Akreuch, Takaddoum, B.P. 5118, Rabat, Marocco

    A. Messaoudi

Authors
  1. K. Jbilou
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  2. A. Messaoudi
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Corresponding author

Correspondence to K. Jbilou .

Editor information

Editors and Affiliations

  1. CESAME, Batiment Euler, Universite Catholique de Louvain, 4, avenue Georges Lemaitre, Louvain la Neuve, 1348, Belgium

    Paul Van Dooren

  2. Department of Electrical and Computer, Engineering, Texas A&M University, Zachry Engineering Center, College Station, 77843-3128, Texas, USA

    Shankar P. Bhattacharyya

  3. Dept. Mathematics, Chinese University Hong Kong, Shatin, New Territories, Hong Kong/PR China

    Raymond H. Chan

  4. Dept. Mathematics, University of Connecticut, Auditorium Road 196, Storrs, 06269-3009, Connecticut, USA

    Vadim Olshevsky

  5. , Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    Aurobinda Routray

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Jbilou, K., Messaoudi, A. (2011). A Computational Method for Symmetric Stein Matrix Equations. In: Van Dooren, P., Bhattacharyya, S., Chan, R., Olshevsky, V., Routray, A. (eds) Numerical Linear Algebra in Signals, Systems and Control. Lecture Notes in Electrical Engineering, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0602-6_14

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  • DOI: https://doi.org/10.1007/978-94-007-0602-6_14

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0601-9

  • Online ISBN: 978-94-007-0602-6

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