Riccati Equation Solution Method for the Computation of the Extreme Solutions of X+A*X-1A=Q and X-A*X-1A=Q

Algebraic and recursive methods for computing the extreme solutions of the matrix equations X + A*X^-1A = Q and X - A*X^-1A = Q are presented in this paper. The proposed algorithms are based on the solution of the corresponding discrete time Riccati equations.