Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic | Zendy

Baur Ulrike | Zendy; Benner Peter | Zendy

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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)

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