On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation

@article{Guo2007OnTD,
  title={On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation},
  author={Chun-Hua Guo and Bruno Iannazzo and Beatrice Meini},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2007},
  volume={29},
  pages={1083-1100}
}
Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible $M$-matrix $M$ are considered. The emphasis is on the case where $M$ is an irreducible singular $M$-matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical interest. The algorithm has been recently studied by others for the case where $M$ is a nonsingular $M$-matrix. A shift technique is proposed… 

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