We are interested in computing the minimal positive solution of a nonsymmetric algebraic Riccati equation arising in transport theory. We show that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from special form of solutions of the Riccati equation. A simple iterative method is presented for solving the vector equation. The simple iteration is much more efficient and effective than some corresponding iterations for the Riccati equation. Symmetric case and bounds of the minimal positive solution are also considered. Numerical experiments are given.
1 Work supported in part by NSF of China.