TY  - JOUR
A1  - Redmann, Martin
A1  - Freitag, Melina A.
T1  - Optimization based model order reduction for stochastic systems
JF  - Applied mathematics and computation
N2  - In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H-2-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 H-2-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.
KW  - Model order reduction
KW  - Stochastic systems
KW  - Optimality conditions
KW  - Sylvester equations
KW  - Levy process
Y1  - 2021
U6  - https://doi.org/10.1016/j.amc.2020.125783
SN  - 0096-3003
SN  - 1873-5649
VL  - 398
PB  - Elsevier
CY  - New York
ER  -