An Alternating Direction Implicit Method for Solving Projected Generalized Continuous-Time Sylvester Equations

We present the generalized low-rank alternating direction implicit method and the low-rank cyclic Smithmethod to solve projected generalized continuous-time Sylvester equations with low-rank right-hand sides. Such equations arise in control theory including the computation of inner products and H 2 norms and the model reduction based on balanced truncation for descriptor systems. The requirements of these methods are moderate with respect to both computational cost and memory. Numerical experiments presented in this paper show the effectiveness of the proposed methods.