The numerical treatment of linear-quadratic regulator problems for
parabolic partial differential equations (PDEs) on infinite time horizons
requires the solution of large scale algebraic Riccati equations (ARE).
The Newton-ADI iteration is an efficient numerical method for this task.
It includes the solution of a Lyapunov equation by the alternating directions
implicit (ADI) algorithm in each iteration step. On finite time
intervals the solution of a large scale differential Riccati equation is required.
This can be solved by a backward differentiation formula (BDF)
method, which needs to solve an ARE in each time step.
Here, we study the selection of shift parameters for the ADI method.
This leads to a rational min-max-problem which has been considered by
many authors. Since knowledge about the complete complex spectrum
is crucial for computing the optimal solution, this is infeasible for the
large scale systems arising from finite element discretization of PDEs.
Therefore several alternatives for computing suboptimal parameters are
discussed and compared for numerical examples.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200701930 |
| Date | 26 November 2007 |
| Creators | Benner, Peter, Mena, Hermann, Saak, Jens |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Rights | Dokument ist für Print on Demand freigegeben |
| Relation | dcterms:isPartOf:Chemnitz Scientific Computing Preprints ; 06-03 |
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