Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms
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.
Nonsymmetric algebraic Riccati equations
matrix equation
M-matrices
Newton method
quadratically convergent algorithms
cyclic reduction
doubling
1-31
Regular Paper
Dario A.
Bini
Dario A. Bini
Bruno
Iannazzo
Bruno Iannazzo
Beatrice
Meini
Beatrice Meini
Federico
Poloni
Federico Poloni
10.4230/DagSemProc.07461.11
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode