Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model
- Li, Tiexiang
- Chu, Eric King-wah
- Juang, Jong
- Lin, Wen-Wei
DOIAbstract
AbstractFor 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 F±≡I-sˆPD±, B-≡(bˆI+sˆP)D- and B+≡bˆI+sˆPD+ with a nonnegative matrix P, positive diagonal matrices D±, and nonnegative parameters f, bˆ≡b/(1-f) and sˆ≡s/(1-f). We prove the existence of the minimal nonnegative solution X∗ under the physically reasonable assumption f+b+s‖P(D++D-)‖∞<1, and study its numerical computation by fixed-point iteration, Newton’s method and doubling. We shall also study several special cases; e.g. when bˆ=0 and P is low-ranked, then X∗=sˆ2UV is low-ranked and can be computed using more efficient iterat...
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