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

Tiexiang Li, King-Wah Eric Chu, Jong Juang, Wen-wei Lin

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

For the steady-state solution of an integral-differential 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 View the MathML source, View the MathML source and View the MathML source with a nonnegative matrix P, positive diagonal matrices DA?, and nonnegative parameters f, View the MathML source and View the MathML source. We prove the existence of the minimal nonnegative solution X* under the physically reasonable assumption View the MathML source, and study its numerical computation by fixed-point iteration, Newton s method and doubling. We shall also study several special cases; e.g. when View the MathML source and P is low-ranked, then View the MathML source 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.
Original languageEnglish
Pages (from-to)201 - 214
Number of pages13
JournalLinear Algebra and Its Applications
Volume434
Issue number1
DOIs
Publication statusPublished - 2011

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