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

Abstract

We survey 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.

Extracted Key Phrases

4 Figures and Tables

Showing 1-10 of 45 references

Canonical and standard forms for certain rank one perturbations and an application to the (complex) Google pageranking problem

  • R A Horn, S Serra, Capizzano
  • 2007
1 Excerpt

Handbook of linear algebra. Discrete Mathematics and its Applications (Boca Raton)

  • Leslie Hogben
  • 2007