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A Multi-Grid Method for Generalized Lyapunov Equations

We present a multi-grid method for a class of
structured generalized Lyapunov matrix equations.
Such equations need to be solved in each step of
the Newton method for algebraic Riccati equations,
which arise from linear-quadratic optimal control
problems governed by partial differential equations.
We prove the rate of convergence of the two-grid
method to be bounded independent of the dimension
of the problem under certain assumptions.
The multi-grid method is based on matrix-matrix
multiplications and thus it offers a great
potential for a parallelization. The efficiency
of the method is demonstrated by numerical
experiments.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200501010
Date07 September 2005
CreatorsPenzl, Thilo
ContributorsTU Chemnitz, SFB 393
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, application/postscript, text/plain, application/zip
SourcePreprintreihe des Chemnitzer SFB 393

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