@Article{JMS-50-54,
author = {Guan , Jinrui and Lu , Linzhang},
title = {New Alternately Linearized Implicit Iteration for M-Matrix Algebraic Riccati Equations},
journal = {Journal of Mathematical Study},
year = {2017},
volume = {50},
number = {1},
pages = {54--64},
abstract = {<p style="text-align: justify;">Research on the theories and the efficient numerical methods of M-matrix
algebraic Riccati equation (MARE) has become a hot topic in recent years due to its
broad applications. In this paper, based on the alternately linearized implicit iteration
method (ALI) [Z.-Z. Bai et al., Numer. Linear Algebra Appl., 13(2006), 655-674.], we
propose a new alternately linearized implicit iteration method (NALI) for computing
the minimal nonnegative solution of M-matrix algebraic Riccati equation. Convergence
of the NALI method is proved by choosing proper parameters for the MARE
associated with nonsingular M-matrix or irreducible singular M-matrix. Theoretical
analysis and numerical experiments show that the NALI method is more efficient than
the ALI method in some cases.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v50n1.17.04},
url = {http://global-sci.org/intro/article_detail/jms/979.html}
}