Abstract
Research on the theories and efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years. In this paper, we consider numerical solution of M-matrix algebraic Riccati equation and propose a modified alternately linearized implicit iteration method (MALI) for computing the minimal nonnegative solution of MARE. Convergence of the MALI method is proved by choosing proper parameters for the nonsingular M-matrix or irreducible singular M-matrix. Theoretical analysis and numerical experiments show that the MALI method is effective and efficient in some cases.
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