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Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic†

  1. Ulrike Baur1,*,
  2. Peter Benner2,*

Article first published online: 27 DEC 2004

DOI: 10.1002/pamm.200410310

Issue

PAMM

PAMM

Volume 4, Issue 1, pages 658–659, December 2004

Additional Information

How to Cite

Baur, U. and Benner, P. (2004), Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic. Proc. Appl. Math. Mech., 4: 658–659. doi: 10.1002/pamm.200410310

Author Information

  1. 1

    Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany

  2. 2

    Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Straße 41, 09107 Chemnitz, Germany

*Phone: +49 (0)30 314 79177, Fax: +49 (0)30 314 79706

  1. †

    Supported by the DFG Research Center “Mathematics for key technologies” (FZT 86) in Berlin.

Publication History

  1. Issue published online: 27 DEC 2004
  2. Article first published online: 27 DEC 2004

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References

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    P. Benner and E. S. Quintana-Ortí. Solving stable generalized Lyapunov equations with the matrix sign function. Numer. Alg., 20(1):75– 100, 1999.
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    C. H. Bischof and G. Quintana-Ortí. Computing rank-revealing QR factorizations of dense matrices. ACM Trans. Math. Software, 24(2):226–253, 1998.
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    R. Byers, C. He, and V. Mehrmann. The matrix sign function method and the computation of invariant subspaces. SIAM J. Matrix Anal. Appl., 18(3):615–632, 1997.
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    L. Grasedyck. Theorie und Anwendungen Hierarchischer Matrizen. PhD thesis, University of Kiel, Germany, 2001.
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    W. Hackbusch. A sparse matrix arithmetic based on ℋ-matrices. I. Introduction to ℋ-matrices. Computing, 62(2):89–108, 1999.
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    W. Hackbusch L. Grasedyck and B. N. Khoromskij. Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Computing, 70(2):121–165, 2003.
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    J. D. Roberts. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Internat. J. Control, 32:677–687, 1980. (Reprint of Technical Report No. TR-13, CUED/B-Control, Cambridge University, Engineering Department, 1971).
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    L. Grasedyck S. Börm and W. Hackbusch. HLib 1.2, 2004. Available from http://www.numerik.uni-kiel.de/∼lgr/gethmatrix.html.
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