NUMERICAL-SOLUTIONS OF THE ALGEBRAIC MATRIX RICCATI EQUATION

The linear-quadratic control model is one of the most widely used cont rol models in both empirical and theoretical economic modeling. In ord er to obtain the equilibrium solution of this control model, the so-ca lled algebraic matrix Riccati equation has to be solved. In this note we present a numerical solution method for solving this equation. Our method solves the Riccati equation as a multidimensional fixed-point p roblem. By establishing the analytical derivative of the Riccati equat ion we have been able to construct a very efficient Newton-type soluti on method with quadratic convergence properties. Our method is an exte nsion for the Newton-Raphson method described in Kwakernaak and Sivan (1972) and does not require any special conditions on the transition m atrix as in the nonrecursive method of Vaughan (1970).