On the solution of the rational matrix equation X = Q + LX-1LT

Authors:
Peter Benner;Heike Faßbender
Affiliations:
Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany;Institut Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2007

Citing 7
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Abstract

We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX-1LT, where Q is symmetric positive definite and L 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 SZ algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.