Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model

@article{Li2011SolutionOA,
  title={Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model},
  author={Tie-xiang Li and Eric King-wah Chu and Jong Juang and Willis Lin},
  journal={Ima Journal of Numerical Analysis},
  year={2011},
  volume={31},
  pages={1453-1467}
}
For the steady-state solution of a differential equation from a one-dimensional multistate model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B− − X F− − F+X + X B+X = 0, where F± ≡ (I − F)D± and B± ≡ B D± with positive diagonal matrices D± and possibly low-ranked matrices F and B. We prove the existence of the minimal positive solution X∗ under a set of physically reasonable assumptions and study its numerical computation by fixed-point iteration… 

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