TY - JOUR

T1 - Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model

AU - Li, Tiexiang

AU - Chu, King-Wah

AU - Juang, Jong

AU - Lin, Wen-wei

PY - 2011

Y1 - 2011

N2 - or 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* = Gamma
circle(Sigma(r)(i=1)U(i)V(i)(T)) with low-ranked U(i) and V(i) that
can be computed using more efficient iterative processes. Numerical
examples will be given to illustrate our theoretical results.

AB - or 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* = Gamma
circle(Sigma(r)(i=1)U(i)V(i)(T)) with low-ranked U(i) and V(i) that
can be computed using more efficient iterative processes. Numerical
examples will be given to illustrate our theoretical results.

UR - http://imajna.oxfordjournals.org/content/early/2011/05/30/imanum.drq034.abstract

U2 - 10.1093/imanum/drq034

DO - 10.1093/imanum/drq034

M3 - Article

VL - 31

SP - 1453

EP - 1467

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

IS - 4

ER -