New Alternately Linearized Implicit Iteration for M-Matrix Algebraic Riccati Equations (Journal of Mathematical Study, 2017)
Research on the theories and the efficient numerical methods of M-matrixalgebraic Riccati equation (MARE) has become a hot topic in recent years due to itsbroad applications. In this paper, based on the alternately linearized implicit iterationmethod (ALI) [Z.-Z. Bai et al., Numer. Linear Algebra Appl., 13(2006), 655-674.], wepropose a new alternately linearized implicit iteration method (NALI) for computingthe minimal nonnegative solution of M-matrix algebraic Riccati equation. Convergenceof the NALI method is proved by choosing proper parameters for the MAREassociated with nonsingular M-matrix or irreducible singular M-matrix. Theoreticalanalysis and numerical experiments show that the NALI method is more efficient thanthe ALI method in some cases.
Keywords: M-matrix algebraic Riccati equation; M-matrix; ALI iteration method.