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Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic
Author(s) -
Baur Ulrike,
Benner Peter
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410310
Subject(s) - mathematics , matrix (chemical analysis) , rank (graph theory) , sign (mathematics) , lyapunov equation , lyapunov function , sign function , function (biology) , mathematical analysis , combinatorics , materials science , physics , nonlinear system , quantum mechanics , evolutionary biology , composite material , biology
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)