Numerical Study on Nonsymmetric Algebraic Riccati Equations

Abstract

In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the Riccati equation is known to have a minimal nonnegative solution. We present two new numerical methods which can be applied directly in the case where K is a regular M-matrix. Furthermore, we find that the alternately linearized implicit iteration method is also feasible. In addition, we study the monotone convergence property of the proposed methods. Numerical experiments show that the above three numerical iteration methods are feasible and effective for solving the nonsymmetric algebraic Riccati equation.