133 Pages

Optimal interpolation-based model reduction [Elektronische Ressource] / von Dorota Kubalińska


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Optimal interpolation-based model reductionvon Dorota Kubalinsk´ aDissertationzur Erlangung des Grades einer Doktorin der Naturwissenschaften– Dr. rer. nat. –Vorgelegt im Fachbereich 3 (Mathematik & Informatik)der Universit¨ at Bremenim September 2008Datum des Promotionskolloquiums: 29.09.2008Gutachter: Prof. Dr. Angelika Bunse-Gerstner, Universit¨ at BremenProf. Dr. Heike Faßbender, Technische Universit¨ at BraunschweigiiiAbstractThis dissertation is devoted to the development and study of new techniques in thefield of model reduction for large-scale linear time-invariant (LTI) dynamical systems.The behavior of processes in electrical networks, mechanics, aeronautics, civil en-gineering, micro-electro-mechanical-systems, weather prediction and many otherscan be described by mathematical models. Such models are usually determined bysuitable systems of partial differential equations. Their linearization and discretiza-tion by means of finite element or finite difference methods lead to high-dimensionalsystems of linear ordinary differential or equations. The number of re-sulting equations depends on the quality of the discretization and is typically verylarge. It can easily reach a few millions.Model reduction methods can then be helpful as they provide automatic processeswhich construct a reduced order system of the same form but of lower complexity,whose input-output behavior approximates the behavior of the original system.



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Published 01 January 2008
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