ℌ2 and ℌ∞ error bounds for model order reduction of second order systems by Krylov subspace methods

We present rigorous bounds on the ℌ₂ and ℌ_∞ norm of the error resulting from model order reduction of second order systems by KRYLOV subspace methods. To this end, we use a strictly dissipative state space realization of the model and perform a factorization of the error system. The derived error expressions are easy to compute and can therefore be applied to models of very high order, as is demonstrated in numerical examples. In fact, all results hold true for arbitrary state space models in strictly dissipative realization that do not necessarily have to originate from second order systems.