On the Solution of the Rational Matrix Equation X=Q+LX−1LT. (10th May 2007) - Benner Benner, Peter Peter; Faßbender Faßbender, Heike Heike
Abstract : We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equationX = Q + L X − 1 L T, whereQ is symmetric positive definite andL is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE). We discuss how to use the butterflyS Z algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.