The projected Newton-Kleinman method for the algebraic Riccati equation

01/29/2019
by   Davide Palitta, et al.
0

The numerical solution of the algebraic Riccati equation is a challenging task especially for very large problem dimensions. In this paper we present a new algorithm that combines the very appealing computational features of projection methods with the convergence properties of the inexact Newton-Kleinman procedure equipped with a line search. In particular, the Newton scheme is completely merged in a projection framework with a single approximation space so that the Newton-Kleinman iteration is only implicitly performed. Moreover, the line search that guarantees the convergence of the inexact procedure to a stabilizing solution turns out to be exact in our setting. This property determines a monotone decrease of the Riccati residual norm under some mild assumptions. Several numerical results are reported to illustrate the potential of our novel approach.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset