## 摘要

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^{-} - 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*=Γ(∑i=14UiViT) with low-ranked Ui and Vi that can be computed using more efficient iterative processes. Numerical examples will be given to illustrate our theoretical results.

原文 | English |
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頁（從 - 到） | 1453-1467 |

頁數 | 15 |

期刊 | IMA Journal of Numerical Analysis |

卷 | 31 |

發行號 | 4 |

DOIs | |

出版狀態 | Published - 10月 2011 |