Optimization based model order reduction for stochastic systems
Martin Redmann and
Melina A. Freitag
Applied Mathematics and Computation, 2021, vol. 398, issue C
Abstract:
In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H2-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error bounds for model order reduction of stochastic differential equations. With these error bounds, we establish a link between the output error for stochastic systems (with additive and multiplicative noise) and modified versions of the H2-norm for both linear and bilinear deterministic systems. When deriving the respective optimality conditions for minimizing the error bounds, we see that model order reduction techniques related to iterative rational Krylov algorithms (IRKA) are very natural and effective methods for reducing the dimension of large-scale stochastic systems with additive and/or multiplicative noise. We apply modified versions of (linear and bilinear) IRKA to stochastic linear systems and show their efficiency in numerical experiments.
Keywords: Model order reduction; Stochastic systems; Optimality conditions; Sylvester equations; Lévy process (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320307360
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300320307360
DOI: 10.1016/j.amc.2020.125783
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().