Numerical solutions of the algebraic matrix Riccati equation

✍ Scribed by Hans M. Amman; Heinz Neudecker

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 349 KB
• Volume: 21
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(96)00936-0

✦ Synopsis

The linear-quadratic control model is one of the most widely used control models in both empirical and theoretical economic modeling. In order to obtain the equilibrium solution of this control model, the so-called 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 problem. By establishing the analytical derivative of the Riccati equation we have been able to construct a very efficient Newton-type solution method with quadratic convergence properties. Our method is an extension for the Newton-Raphson method described in Kwakemaak and Sivan ( 1972) and does not require any special conditions on the transition rn3 as inthe nonrecursive method of Vaughan (1970).