Frequency- and time-limited balanced truncation for large-scale second-order systems

Considering the use of dynamical systems in practical applications, often only limited regions time or frequency domain are interest. Therefor, it usually pays off to compute local approximations used and domain. In this paper, we consider a structure-preserving extension frequency- time-limited balanced truncation methods second-order systems. We give full overview about first-order extend those by using different formulas from literature. Also, present numerical for solving arising large-scale sparse matrix equations modifications deal with problematic case The results then illustrated on three examples.