Year: 2017
Author: Jinrui Guan, Linzhang Lu
Journal of Mathematical Study, Vol. 50 (2017), Iss. 1 : pp. 54–64
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v50n1.17.04
Journal of Mathematical Study, Vol. 50 (2017), Iss. 1 : pp. 54–64
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: M-matrix algebraic Riccati equation M-matrix ALI iteration method.