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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18351 |
| Date | 07 September 2005 |
| Creators | Penzl, Thilo |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Source | Preprintreihe des Chemnitzer SFB 393 |
| Rights | info:eu-repo/semantics/openAccess |
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