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