On the Solution of the Rational Matrix Equation X=Q+LX−1LT. (10th May 2007)

• Record Type: Journal Article
• Authors: Benner Benner, Peter Peter; Faßbender Faßbender, Heike Heike
• Other Names: Van Dooren Van Dooren Paul Paul Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2007(2007)
• Publication Date: 2007-05-10
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2007/21850
• Languages: English
• ISSNs: 1687-6172

Abstract

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.