A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory

In this paper, we consider the nonsymmetric algebraic Riccati equation arising in transport theory. An important feature of this equation is that its minimal positive solution can be obtained via computing the minimal positive solution of a vector equation. We propose a class of iterative methods to solve the vector equation. The convergence analysis shows that the sequence of vectors generated by iterative methods with two kinds of specific iterative matrices is monotonically increasing and converges to the minimal positive solution of the vector equation. Numerical experiments show that the new methods outperform the modified simple iterative method and Newton’s method.