A framework for the solution of the generalized realization problem

By Anita Mayo, Athanasios C. Antoulas. 2007

466 citations recorded by the source corpus.

In this paper we present a novel way of constructing generalized state space representations [E, A, B, C, D] of interpolants matching tangential interpolation data. The Loewner and shifted Loewner matrices are the key tools in this approach.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2863457387d8bc2ba4c9e354b2087b050e392b45

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In Numerical Analysis

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Projection-based model reduction: Formulations for physics-based machine learning (2019, methodology): “Loewner framework [30, 31, 32, 33, 34] provides a more flexible approach by learning reduced models from frequency-response data (i.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “For the case of dynamical systems with no parametric dependence, the Loewner-based data-driven framework [148, 149, 171] has been applied with great success to construct reduced models using only transfer function samples.”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, background): “, from transfer function evaluations [12, 13, 14], without requiring the operators of the full LTI system.”