License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07461.11
URN: urn:nbn:de:0030-drops-13958
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1395/
Go to the corresponding Portal

Bini, Dario A. ; Iannazzo, Bruno ; Meini, Beatrice ; Poloni, Federico

Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms

pdf-format:
07461.IannazzoBruno.Paper.1395.pdf (0.3 MB)

Abstract

We survey on theoretical properties and algorithms concerning the problem of solving a nonsymmetric algebraic Riccati equation, and we report on some known methods and new algorithmic advances. In particular, some results on the number of positive solutions are proved and a careful convergence analysis of Newton's iteration is carried out in the cases of interest where some singularity conditions are encountered. From this analysis we determine initial approximations which still guarantee the quadratic convergence.

BibTeX - Entry

@InProceedings{bini_et_al:DagSemProc.07461.11,
  author =	{Bini, Dario A. and Iannazzo, Bruno and Meini, Beatrice and Poloni, Federico},
  title =	{{Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--31},
  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/2008/1395},
  URN =		{urn:nbn:de:0030-drops-13958},
  doi =		{10.4230/DagSemProc.07461.11},
  annote =	{Keywords: Nonsymmetric algebraic Riccati equations, matrix equation, M-matrices, Newton method, quadratically convergent algorithms, cyclic reduction, doubling}
}

Keywords: Nonsymmetric algebraic Riccati equations, matrix equation, M-matrices, Newton method, quadratically convergent algorithms, cyclic reduction, doubling
Collection: 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