On the Solution of the Rational Matrix Equation X=Q+LX−1LT

Autor: Heike Faßbender, Peter Benner
Jazyk: angličtina
Rok vydání: 2007
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Zdroj: EURASIP Journal on Advances in Signal Processing, Vol 2007 (2007)
Druh dokumentu: article
ISSN: 1687-6172
1687-6180
DOI: 10.1155/2007/21850
Popis: 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.
Databáze: Directory of Open Access Journals
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