Two-parameters numerical methods of the non-symmetric algebraic Riccati equation

In this paper, we focus on finding the minimal non-negative solution of a certain class of non-symmetric algebraic Riccati equations whose four coefficient matrices form a regular M-matrix. Firstly, we present two new numerical algorithms called modified inexact Newton method (MINewton) and modified structure-preserving doubling method (MSDA). Then we introduce two parameters in these algorithms, and establish the convergence theory by using Cayley transformation. Finally we give some numerical results to show the effectiveness of our derived methods compared with other iteration methods.