A PRACTICAL IMPLEMENTATION FOR SOLUTIONS TO THE ALGEBRAIC MATRIX RICCATI EQUATION IN A LQCM SETTING

The linear-quadratic control model (LQCM) is very popular due to its a pplicability to many economic situations. An infinite-horizon equilibr ium solution to such a model requires that we solve the algebraic matr ix Riccati Equation. Numerical methods based on a modified Newton-Raph son iteration converge quadratically to this solution. We show that th e computational complexity of each iteration can be substantially redu ced from O(n(6)) to O(n(4)) by applying Broyden's method of rank-1 upd ates. This method achieves superlinear convergence. Moreover, it maint ains the generality of the original method in that it does not impose constraints on matrix structure. (C) 1998 Elsevier Science B.V. All ri ghts reserved.