Open Access

On the Solution of the Rational Matrix Equation

EURASIP Journal on Advances in Signal Processing20072007:021850

Received: 30 September 2006

Accepted: 22 February 2007

Published: 10 May 2007


We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation , where is symmetric positive definite and 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 butterfly algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.


Authors’ Affiliations

Fakultät für Mathematik, Technische Universität Chemnitz
Institut Computational Mathematics, Technische Universität Braunschweig


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© P. Benner and H. Faßbender 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.