### Abstract

or 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(-) -XF(-) -F(+)
X + XB(+)X = 0, where F(+/-) = (I -F) D(+/-) and B(+/-) = BD(+/-) 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, Newton s method and
the doubling algorithm. We shall also study several special cases. For
example when B and F are low ranked then X* = Gamma
circle(Sigma(r)(i=1)U(i)V(i)(T)) with low-ranked U(i) and V(i) that
can be computed using more efficient iterative processes. Numerical
examples will be given to illustrate our theoretical results.

Original language | English |
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Pages (from-to) | 1453 - 1467 |

Number of pages | 15 |

Journal | IMA Journal of Numerical Analysis |

Volume | 31 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 |

## Cite this

Li, T., Chu, K-W., Juang, J., & Lin, W. (2011). Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model.

*IMA Journal of Numerical Analysis*,*31*(4), 1453 - 1467. https://doi.org/10.1093/imanum/drq034