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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

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PAMM

PAMM

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

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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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Abstract

We investigate the solution of the Lyapunov equation with the matrix sign function method. In order to obtain the factorized solution we use a partitioned Newton iteration, where one part of the iteration uses formatted arithmetic for the hierarchical matrix format while the other part converges to an approximate full-rank factor of the solution. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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