@Article{AAMM-9-4,
author = {Ning, Dong and Jin, Jicheng and Yu, Bo},
title = {Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {4},
pages = {944--963},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1277},
url = {https://global-sci.com/article/73286/convergence-rates-of-a-class-of-predictor-corrector-iterations-for-the-nonsymmetric-algebraic-riccati-equation-arising-in-transport-theory}
}