The relaxed Newton-like method for a nonsymmetric algebraic Riccati equation

The non-symmetric algebraic Riccati equation arising in transport theory can be rewritten as a vector equation and the minimal positive solution of the non-symmetric algebraic Riccati equation can be obtained by solving the vector equation. In this paper; based on the relaxation technique; we propose a relaxed Newton-like method containing a relaxation parameter for solving the vector equation. Some convergence results are presented. The convergence analysis shows that sequence of vectors generated by the relaxed Newton-like method is monotonically increasing and converges to the minimal positive solution of the vector equation. Finally; numerical experiments are reported.