Splitting iteration methods to solve non-symmetric algebraic Riccati matrix equation YAY - YB - CY + D=0

The non-symmetric algebraic Riccati equation (NARE) occurs in several areas of applied mathematics and engineering such as spectral factorizations of rational matrix functions, constructive rational matrix functions, transport theory, optimal controls, and structured stability radius. Using new weight splitting on matrices, we propose several efficient iterative methods for computing a solution of the NARE. Under suitable conditions, the proposed methods converge to the minimal non-negative solution of the NARE. Numerical examples indicate that the proposed methods are superior to the alternately linearized implicit iteration method and other splitting methods in terms of computational cost, accuracy, and CPU time.