A practical implementation for solutions to the algebraic matrix Riccati equation in a LQCM setting

✍ Scribed by R.B. Carroll; D.A. Brask

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 92 KB
• Volume: 23
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(98)00002-5

✦ Synopsis

The linear-quadratic control model (LQCM) is very popular due to its applicability to many economic situations. An infinite-horizon equilibrium solution to such a model requires that we solve the algebraic matrix Riccati Equation. Numerical methods based on a modified Newton-Raphson iteration converge quadratically to this solution. We show that the computational complexity of each iteration can be substantially reduced from O(n) to O(n) by applying Broyden's method of rank-1 updates. This method achieves superlinear convergence. Moreover, it maintains the generality of the original method in that it does not impose constraints on matrix structure.