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URN: urn:nbn:de:0030-drops-13958
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1395/
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Bini, Dario A. ; Iannazzo, Bruno ; Meini, Beatrice ; Poloni, Federico

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

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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:DSP:2008:1395,
  author =	{Dario A. Bini and Bruno Iannazzo and Beatrice Meini and Federico Poloni},
  title =	{Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  year =	{2008},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  number =	{07461},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1395},
  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
Seminar: 07461 - Numerical Methods for Structured Markov Chains
Issue Date: 2008
Date of publication: 07.04.2008


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