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 -