Abstract
This paper proposes two algorithms (Algorithm I and Algorithm II) for solving a stochastic discrete algebraic Riccati equation, which arises in stochastic optimal control for the discrete-time system. Our algorithms are generalized versions of Hewer's algorithm. Algorithm I has the quadratic convergence but requires to solve a sequence of non-standard Lyapunov equations. On the other hand, Algorithm II needs the solutions of standard discrete Lyapunov equations, which can be solved easily, but it has a linear convergent term. By a numerical example, it is shown that Algorithm I is superior to Algorithm II in the case of large dimension.
