Conference Agenda
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RApp: Rational approximation as an effective tool for tackling practical problems Location: D301 Session Chair: Jan Heiland Session Chair: Ion Victor Gosea | |
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Interpolatory Model Reduction in Reproducible Kernel Hilbert Spaces 1: UniDistance Suisse, Switzerland; 2: King Abdullah University of Science and Technology, Saudi Arabia We consider the problem of model order reduction in reproducible kernel Hilbert spaces (RKHSs). We prove a generalization of well-known necessary interpolatory conditions for norm-optimal reduced order models, originally stated for rational functions in the Hardy-Hilbert space $H_2$. Previous optimality conditions stated for $H_2$ spaces defined over various domains (e.g., the disk and the half plane) are special cases of the condition obtained in this talk. We introduce generalized Malmquist-Takenaka (GMT) functions that can be used to define orthonormal bases in an arbitrary RKHS. Using GMT functions, we construct an equivalent alternative to the iterative rational Krylov algorithm for RKHSs with shift invariant kernels to obtain norm-optimal reduced order models. In order to deal with non-shift invariant kernels, we propose a family of unitary transformations using GMT functions. The effectiveness of the proposed methods is demonstrated in several numerical experiments such as linear and nonlinear dynamical systems and machine learning models such as support vector machines and deep ReLU networks. | |
