In this talk we will survey methods for the approximation of large-scale dynamical systems. There are two basic families, namely the SVD-based and Krylov-based approximation methods. The former family is based on the singular value decomposition and the second on moment matching. While the former has many desirable properties including an error bound, it cannot be applied to systems of high complexity. The strength of the latter on the other hand, is that it can be implemented iteratively and is thus appropriate for application to high complexity systems. An effort to combine the best attributes of these two families leads to a third class of approximation methods, which will be referred to as SVD/Krylov. The talk will survey these methods and conclude with a new result concerning model reduction with preservation of passivity which is appropriate for application to large-scale circuits arising in VLSI chip performance verification.
