Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Bini, Dario A.; Meini, Beatrice; Poloni, Federico License
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-13987
URL:

; ;

From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms

pdf-format:


Abstract

The problem of reducing an algebraic Riccati equation $XCX-AX-XD+B=0$ 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 shrink-and-shift tech-
nique of Ramaswami is presented. Finally, faster algorithms which require
some non-singularity conditions, are designed. The non-singularity re-
striction is relaxed by introducing a suitable similarity transformation of
the Hamiltonian.


BibTeX - Entry

@InProceedings{bini_et_al:DagSemProc.07461.7,
  author =	{Bini, Dario A. and Meini, Beatrice and Poloni, Federico},
  title =	{{From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2008/1398},
  URN =		{urn:nbn:de:0030-drops-13987},
  doi =		{10.4230/DagSemProc.07461.7},
  annote =	{Keywords: Algebraic Riccati Equation, Matrix Equation, Cyclic Reduction, Structured doubling algorithm}
}

Keywords: Algebraic Riccati Equation, Matrix Equation, Cyclic Reduction, Structured doubling algorithm
Seminar: 07461 - Numerical Methods for Structured Markov Chains
Issue date: 2008
Date of publication: 07.04.2008


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI