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

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