Acceleration of the New Iterative Method of Solving the Algebraic Riccati Equation Arising in Transport Theory

We are interested in numerically computing the minimal positive solution of a nonsymmetric algebraic Riccati equation (NARE) arising in transport theory. The new iterative method of Y. Lin (Computers and Mathematics with Applications 56, 2008, 3046-3051) succeeds to find this solution via computing the minimal positive solution of a vector equation. On the other hand, the convergence of the iterative scheme proposed by this method tends to be slow in critical cases, as $(\alpha, c)$ aproaches to $(0,1)$. Here, a small modification is made to the iterative scheme which leads to a faster convergence, especially in critical cases. Numerical results are given to verify the efficiency of the proposed approach.