The iterative solution to LQ zero-sum stochastic differential games

We consider a generalized algebraic Riccati equation arising in stochastic control with an indefinite quadratic part. Three effective methods for computing a matrix sequence, which converges to the stabilizing solution of the considered type of Riccati equations with indefinite quadratic parts are explored. Convergence properties of these methods are studied. Computer realizations of the presented methods are numerically compared. Based on the experiments the main conclusion is that the Lyapunov iteration is faster than the Riccati iteration because these methods carry the same number of iterations. The iterative methods are numerically compared and investigated.