eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-04-07
1
31
10.4230/DagSemProc.07461.11
article
Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms
Bini, Dario A.
Iannazzo, Bruno
Meini, Beatrice
Poloni, Federico
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol07461/DagSemProc.07461.11/DagSemProc.07461.11.pdf
Nonsymmetric algebraic Riccati equations
matrix equation
M-matrices
Newton method
quadratically convergent algorithms
cyclic reduction
doubling