Kolmogorov n-widths for linear dynamical systems

• Published in: Advances in computational mathematics Vol. 45; no. 5-6; pp. 2273 - 2286
• Main Authors: Unger, Benjamin, Gugercin, Serkan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2019; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Dynamical systems; Lower bounds; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Model reduction; Model reduction of parametrized Systems; Subspaces; Visualization; 37M99; 65P99; 34A45; 35A35; 93C05; 47B35; Kolmogorov; width; Active subspaces; Model reduction; Hankel operator; Reduced basis method; Hankel singular values

Kolmogorov n -widths and Hankel singular values are two commonly used concepts in model reduction. Here, we show that for the special case of linear time-invariant (LTI) dynamical systems, these two concepts are directly connected. More specifically, the greedy search applied to the Hankel operator...