  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.
