On the solution of the radical matrix equation $X=Q+LX^{-1}L^T$

Description

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.

Links & Downloads

1. urn:nbn:de:bsz:ch1-200701929
2. 1864-0087
3. https://monarch.qucosa.de/id/qucosa%3A18829
4. https://monarch.qucosa.de/api/qucosa%3A18829/attachment/ATT-0/
5. https://monarch.qucosa.de/api/qucosa%3A18829/attachment/ATT-1/

Tags

info:eu-repo/classification/ddc/510

ddc:510

Matrix <Mathematik>

Nichtlineare algebraische Gleichung

butterfly SZ algorithm

discrete-time algebraic Riccati equation

nonlinear matrix equation

Additional Fields

Identifer	oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18829
Date	26 November 2007
Creators	Benner, Peter, Faßbender, Heike
Publisher	Technische Universität Chemnitz
Source Sets	Hochschulschriftenserver (HSSS) der SLUB Dresden
Language	English
Detected Language	English
Type	doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
Rights	info:eu-repo/semantics/openAccess