A novel linear iteration method for M-matrix algebraic Riccati equations

GUAN Jinrui; FENG Yuehua

doi:10.3969/j.issn.0253-2778.2020.12.004

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Open Access JUSTC Research Article

A novel linear iteration method for M-matrix algebraic Riccati equations

1.
Department of Mathematics, Taiyuan Normal University,Jinzhong 030619, China
2.
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science,Shanghai 201620 China

Funds: The work is supported by National Natural Science Foundation of China (12001363, 12001395), Natural Science Foundation of Shanxi province, China (201901D211423).

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https://doi.org/10.3969/j.issn.0253-2778.2020.12.004

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Corresponding author: Guan Jinrui ( corresponding author ) is now an associate professor at Departement of Mathematics, Taiyuan Normal University, China. He received his Ph. D. degree in computational mathematics at Xiamen University in 2016. His research interests focus on matrix theory and numerical linear algebra with applications.
Received Date: 10 October 2020
Accepted Date: 24 November 2020
Publish Date: 30 December 2020

Abstract Full text PDF

Abstract

Abstract

Numerical solutions of the M-matrix algebraic Riccati equation (MARE) were studied, which has become a hot topic in recent years due to its broad applications. A novel linear iteration method for computing the minimal nonnegative solution of MARE was proposed, in which only matrix multiplications are needed at each iteration. Convergence of the new method was proved by choosing proper parameters for the MARE associated with a nonsingular M-matrix or an irreducible singular M- matrix. Theoretical analysis and numerical experiments show that the new method is feasible and is effective than some existing methods under certain conditions.

Abstract

Numerical solutions of the M-matrix algebraic Riccati equation (MARE) were studied, which has become a hot topic in recent years due to its broad applications. A novel linear iteration method for computing the minimal nonnegative solution of MARE was proposed, in which only matrix multiplications are needed at each iteration. Convergence of the new method was proved by choosing proper parameters for the MARE associated with a nonsingular M-matrix or an irreducible singular M- matrix. Theoretical analysis and numerical experiments show that the new method is feasible and is effective than some existing methods under certain conditions.