Frequency Limited $\mathcal{H}_2$ Optimal Model Reduction of Large-Scale Sparse Dynamical Systems

We mainly consider the frequency limited $\mathcal{H}_2$ optimal model order reduction of large-scale sparse generalized systems. For this purpose we need to solve two Sylvester equations. This paper proposes efficient algorithm to solve them efficiently. The ideas are also generalized to index-1 descriptor systems. Numerical experiments are carried out using Python Programming Language and the results are presented to demonstrate the approximation accuracy and computational efficiency of the proposed techniques.