On the numerical solution of large-scale sparse discrete-time Riccati equations

The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton’s method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute lowrank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.