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

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



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Dario A. Bini
Bruno Iannazzo
Beatrice Meini
Federico Poloni

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Dario A. Bini, Bruno Iannazzo, Beatrice Meini, and Federico Poloni. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-31, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/DagSemProc.07461.11

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.
Keywords
  • Nonsymmetric algebraic Riccati equations
  • matrix equation
  • M-matrices
  • Newton method
  • quadratically convergent algorithms
  • cyclic reduction
  • doubling

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