We study numerical methods for finding the maximal
symmetric positive definite solution of the nonlinear matrix equation
$X = Q + LX^{-1}L^T$, 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 type iterative methods suggested in the
literature.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200701929 |
| Date | 26 November 2007 |
| Creators | Benner, Peter, Faßbender, Heike |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Rights | Dokument ist für Print on Demand freigegeben |
| Relation | dcterms:isPartOf:Chemnitz Scientific Computing Preprints ; 06-02 |
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