An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems

We propose a model reduction algorithm which combines the SVD and Krylov-based techniques. It is a two-sided projection method where one side carries the SVD (Gramian) information and the other side the Krylov information. While the SVD-side depends on the observability gramian, the Krylov-side is obtained via iterative rational Krylov steps. The reduced model is asymptotically stable and matches the moments of the original system at the mirror images of the reduced system poles; hence it is the best H2approximation among all reduced models having the same reduced system poles. Numerical results proves the effectiveness of the proposed approach.