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Modeling strategies often result in dynamical systems of very high dimension. It is then desirable to find systems of the same form but of lower complexity, whose input-output behavior approximates the behavior of the original system. Here we consider linear time invariant (LTI) discrete time dy-namical systems. The cornerstone of this paper is a relation(More)
We present rigorous a posteriori output error bounds for reduced basis approximations of parametrized parabolic partial differential equations with non-affine source terms. The method employs the empirical interpolation method in order to construct affine coefficient-function approximations of the non-affine parametrized functions. Our a posteriori error(More)
This paper deals with H 2-norm optimal model reduction for linear time invariant continuous MIMO systems. We will give an overview on several representations of linear systems in state space as well as in Laplace space and discuss the H 2-norm for continuous MIMO systems with multiple poles. On this basis, necessary optimality conditions for the H 2-norm(More)
The main focus of this paper is on an a-posteriori analysis for different model-order strategies applied to optimal control problems governed by linear parabolic partial differential equations. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the reduced-order model, is from the (unknown) exact one. For(More)
E-learning environments and their functionalities presently resemble one another to a large extent. Recent standardization efforts in e-learning concentrate on the reuse of learning material, but not on the reuse of application or system functionalities. The LearnServe system under development at the University of Muenster builds on the assumption that a(More)
In this paper the equivalences between necessary optimality conditions for H 2-norm optimal model reduction for linear time invariant continuous MIMO systems will be proven. Initially three main optimality conditions, namely the Interpolation conditions, Wilson conditions and Hyland-Bernstein conditions, were introduced. While the equivalence proof between(More)
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