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Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms Bini, Dario A. Iannazzo, Bruno Meini, Beatrice Poloni, Federico Nonsymmetric algebraic Riccati equations matrix equation M-matrices Newton method quadratically convergent algorithms cyclic reduction doubling 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dario A. Bini and Bruno Iannazzo and Beatrice Meini and Federico Poloni 2008 Is Part Of Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.07461.11 urn:nbn:de:0030-drops-13958 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.11 eng https://creativecommons.org/licenses/by/4.0/legalcode