Efficient balance-and-truncate model reduction for large scale systems

We present efficient implementations of the balance-and-truncate model reduction technique for large-scale systems. The key observation that distinguishes our approach is that Krylov subspace methods (Arnoldi and Lanczos) directly yield approximate low-rank square roots of the system Gramians; the balancing transformation can then be constructed from these square roots, obviating the need for solving any Lyapunov equations. In addition, the order of the reduced model is not fixed a priori as with some existing methods, but is determined from the problem data. Numerical simulations show that our approach performs very well over a range of examples, and offers considerable savings in practice.