Model reduction for large-scale dynamical systems via equality constrained least squares

In this paper, we present a new method of model reduction for large-scale dynamical systems, which belongs to the SVD–Krylov based method category. It is a two-sided projection where one side reflects the Krylov part and the other side reflects the SVD (observability gramian) part. The reduced model matches the first r+ir+i Markov parameters of the full order model, and the remaining ones approximate in a least squares sense without being explicitly computed, where rr is the order of the reduced system, and ii is a nonnegative integer such that 1≤i