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.

Key words: algebraic Riccati equation, M-matrix, minimal nonnegative solution, Newton method, doubling algorithm