Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model
Resource
IMA Journal of Numerical Analysis, 31(4), 1453-1467
Journal
IMA Journal of Numerical Analysis
Pages
1453-1467
Date Issued
2011
Date
2011
Author(s)
Li, Tiexiang
Chu, Eric King-Wah
Juang, Jong
Lin, Wen-Wei
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.
Type
journal article
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