On Error Estimation for Reduced-order Modeling of Linear Non-parametric and Parametric Systems

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It has been shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate output error of reduced-order modeling for steady linear parametric systems.
Comment: 34 pages, 12 figures