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

Tiexiang Li Eric King-wah Chu Jong Juang Wen-Wei Lin

Numerical Analysis and Scientific Computing mathscidoc:1912.43740

Linear Algebra and its Applications, 434, (1), 201-214, 2011.1
For the steady-state solution of an integraldifferential equation from a two-dimensional model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B--XF--F+ X+ XB+ X= 0, where F I-s PD, B-(b I+ s P) D-and B+ b I+ s PD+ with a nonnegative matrix P, positive diagonal matrices D, and nonnegative parameters f, b b/(1-f) and s s/(1-f). We prove the existence of the minimal nonnegative solution X under the physically reasonable assumption f+ b+ s P (D++ D-)< 1, and study its numerical computation by fixed-point iteration, Newtons method and doubling. We shall also study several special cases; eg when b = 0 and P is low-ranked, then X= s 2 UV is low-ranked and can be computed using more efficient iterative processes in U and V. Numerical examples will be given to illustrate our theoretical results.
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@inproceedings{tiexiang2011solution,
  title={Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model},
  author={Tiexiang Li, Eric King-wah Chu, Jong Juang, and Wen-Wei Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205425836960304},
  booktitle={Linear Algebra and its Applications},
  volume={434},
  number={1},
  pages={201-214},
  year={2011},
}
Tiexiang Li, Eric King-wah Chu, Jong Juang, and Wen-Wei Lin. Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model. 2011. Vol. 434. In Linear Algebra and its Applications. pp.201-214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205425836960304.
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