Bini, Dario A. ;
Meini, Beatrice ;
Poloni, Federico
From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms
Abstract
The problem of reducing an algebraic Riccati equation $XCXAXXD+B=0$ to a unilateral quadratic matrix equation (UQME) of the
kind $PX^2+QX+R$ is analyzed. New reductions are introduced
which enable one to prove some theoretical and computational properties.
In particular we show that the structure preserving doubling algorithm
of B.D.O. Anderson [Internat. J. Control, 1978] is nothing else but the
cyclic reduction algorithm applied to a suitable UQME. A new algorithm
obtained by complementing our reductions with the shrinkandshift tech
nique of Ramaswami is presented. Finally, faster algorithms which require
some nonsingularity conditions, are designed. The nonsingularity re
striction is relaxed by introducing a suitable similarity transformation of
the Hamiltonian.
BibTeX  Entry
@InProceedings{bini_et_al:DSP:2008:1398,
author = {Dario A. Bini and Beatrice Meini and Federico Poloni},
title = {From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms},
booktitle = {Numerical Methods for Structured Markov Chains},
year = {2008},
editor = {Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and MarieAnge Remiche and Peter Taylor},
number = {07461},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1398},
annote = {Keywords: Algebraic Riccati Equation, Matrix Equation, Cyclic Reduction, Structured doubling algorithm}
}
2008
Keywords: 

Algebraic Riccati Equation, Matrix Equation, Cyclic Reduction, Structured doubling algorithm 
Seminar: 

07461  Numerical Methods for Structured Markov Chains

Related Scholarly Article: 


Issue date: 

2008 
Date of publication: 

2008 