Speaker: Valeria Simoncini Affiliation: Dipartimento di Matematica, Universita' di Bologna Title: Advances in numerical projection methods for Model Order Reduction of large-scale linear dynamical systems In this talk we shall report on recent results on approximating quantities that are of interest in the development of numerical reduction strategies of large-scale linear dynamical systems. In particular, for non-symmetric and dissipative matrices, we shall concentrate on the solution of algebraic Lyapunov equations, on the approximation of the transfer function and on balanced truncation. Numerical experiments demonstrating the performance of the discussed methods will also be described.