A greedy rational Krylov method for ℋ2-pseudooptimal model order reduction with preservation of stability
We present a new approach to the problem of finding suitable expansion points in Krylov subspace methods for the model reduction of LTI systems. Using a factorized formulation of the resulting error model, we can efficiently apply a greedy algorithm and perform multiple reduction steps instead of lo...
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| creator | Panzer, Heiko K. F. Jaensch, Stefan Wolf, Thomas Lohmann, Boris |
| description | We present a new approach to the problem of finding suitable expansion points in Krylov subspace methods for the model reduction of LTI systems. Using a factorized formulation of the resulting error model, we can efficiently apply a greedy algorithm and perform multiple reduction steps instead of looking for all shifts at once. An expedient globally convergent optimization algorithm delivers locally ℋ 2 -optimal two-dimensional ROMs in each step. The overall ROM, whose error decreases monotonically, is ℋ 2 -pseudooptimal and guaranteed to be stable; its order can be chosen on-the-fly. Ready-to-run Matlab demo code is provided in the Appendix. |
| doi_str_mv | 10.1109/ACC.2013.6580700 |
| format | Conference Proceeding |
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F.</creatorcontrib><creatorcontrib>Jaensch, Stefan</creatorcontrib><creatorcontrib>Wolf, Thomas</creatorcontrib><creatorcontrib>Lohmann, Boris</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Panzer, Heiko K. F.</au><au>Jaensch, Stefan</au><au>Wolf, Thomas</au><au>Lohmann, Boris</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>A greedy rational Krylov method for ℋ2-pseudooptimal model order reduction with preservation of stability</atitle><btitle>2013 American Control Conference</btitle><stitle>ACC</stitle><date>2013-06</date><risdate>2013</risdate><spage>5512</spage><epage>5517</epage><pages>5512-5517</pages><issn>0743-1619</issn><eissn>2378-5861</eissn><isbn>1479901776</isbn><isbn>9781479901777</isbn><eisbn>9781479901753</eisbn><eisbn>147990175X</eisbn><eisbn>1479901784</eisbn><eisbn>9781479901784</eisbn><abstract>We present a new approach to the problem of finding suitable expansion points in Krylov subspace methods for the model reduction of LTI systems. Using a factorized formulation of the resulting error model, we can efficiently apply a greedy algorithm and perform multiple reduction steps instead of looking for all shifts at once. An expedient globally convergent optimization algorithm delivers locally ℋ 2 -optimal two-dimensional ROMs in each step. The overall ROM, whose error decreases monotonically, is ℋ 2 -pseudooptimal and guaranteed to be stable; its order can be chosen on-the-fly. Ready-to-run Matlab demo code is provided in the Appendix.</abstract><pub>IEEE</pub><doi>10.1109/ACC.2013.6580700</doi><tpages>6</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Mathematical model Mirrors Optimization Read only memory Reduced order systems Sparks Vectors |
| title | A greedy rational Krylov method for ℋ2-pseudooptimal model order reduction with preservation of stability |
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