LAUSR

In this paper, we present a new approach for large-scale Lyapunov matrix equations, where we present two algorithms named: Adaptive Block Tangential Lanczos-type and Arnoldi-type algorithms (ABTL and ABTA). This approach is based on the projection of the initial problem onto tangential Krylov subspaces to produce a low-rank approximate solution of large Lyapunov equations. These approximations are used in model reduction of large-scale dynamical systems with multiple inputs and multiple outputs (MIMO). We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms.