TY - JOUR
T1 - New Alternately Linearized Implicit Iteration for M-Matrix Algebraic Riccati Equations
AU - Guan , Jinrui
AU - Lu , Linzhang
JO - Journal of Mathematical Study
VL - 1
SP - 54
EP - 64
PY - 2017
DA - 2017/03
SN - 50
DO - http://doi.org/10.4208/jms.v50n1.17.04
UR - https://global-sci.org/intro/article_detail/jms/979.html
KW - M-matrix algebraic Riccati equation, M-matrix, ALI iteration method.
AB - <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>