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

Tiexiang Li, Eric King Wah Chu*, Juang Jonq, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1453-1467
Number of pages15
JournalIMA Journal of Numerical Analysis
Volume31
Issue number4
DOIs
StatePublished - 1 Oct 2011

Keywords

  • Newton's method
  • algebraic Riccati equation
  • doubling algorithm
  • fixed-point iteration
  • reflection
  • transport theory

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