TY - JOUR
T1 - Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model
AU - Li, Tiexiang
AU - Chu, King-Wah Eric
AU - Juang, Jong
AU - Lin, Wen-wei
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.sciencedirect.com/science/article/pii/S0024379510004593
U2 - 10.1016/j.laa.2010.09.006
DO - 10.1016/j.laa.2010.09.006
M3 - Article
SN - 0024-3795
VL - 434
SP - 201
EP - 214
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1
ER -