In search of frequency-limited low-rank Gramian factors for the balancing based model reduction of large-scale sparse descriptor system

This paper discusses frequency limited balanced truncation of a class of large-scale sparse descriptor system by preserving the sparsity of the system. For this purpose we compute the low-rank Gramian factors by solving the frequency limited Lyapunov equations. We modify the standard rational Krylov subspace method (RKSM) for solving the Lyapunov equations efficiently and implicitly. Several data of index-l descriptor system models are nominated for numerical experiments to demonstrate the efficiency of the proposed techniques.