TY - JOUR
T1 - Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory
AU - Dong , Ning
AU - Jin , Jicheng
AU - Yu , Bo
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 944
EP - 963
PY - 2018
DA - 2018/05
SN - 9
DO - http://doi.org/10.4208/aamm.2015.m1277
UR - https://global-sci.org/intro/article_detail/aamm/12184.html
KW - Convergence rate, predictor-corrector iterations, nonsymmetric algebraic Riccati equation, regular splitting.
AB - <p style="text-align: justify;">In this paper, we analyse the convergence rates of several different predictor-corrector
iterations for computing the minimal positive solution of the nonsymmetric
algebraic Riccati equation arising in transport theory. We have shown theoretically
that the new predictor-corrector iteration given in [Numer. Linear Algebra Appl., 21
(2014), pp. 761–780] will converge no faster than the simple predictor-corrector iteration
and the nonlinear block Jacobi predictor-corrector iteration. Moreover, the last
two have the same asymptotic convergence rate with the nonlinear block Gauss-Seidel
iteration given in [SIAM J. Sci. Comput., 30 (2008), pp. 804–818]. Preliminary numerical
experiments have been reported for the validation of the developed comparison
theory.</p>