A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-183870 |
| Date | 05 November 2015 |
| Creators | Lang, Norman, Saak, Jens, Stykel, Tatjana |
| Contributors | TU Chemnitz, Fakultät für Mathematik, MPI für Dynamik komplexer technischer Systeme,, Universität Magdeburg, 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 |
| Relation | dcterms:isPartOf:Chemnitz Scientific Computing Preprints ; 15-05 |
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