ARE-type iterations for rational Riccati equations arising in stochastic control

We consider the solution of the rational matrix equations, or generalized algebraic Riccati equations with rational terms, arising in stochastic optimal control in continuous-and discrete-time. The modified Newton´s methods, the DARE-and CARE-type iterations for continuous- and discrete-time rational Riccati equations respectively, will be considered. In particular, the convergence of these new modified Newton´s method will be proved.