On the iterative solution of a class of nonsymmetric algebraic Riccati equations (Q2706263)

The authors present an new algorithm for iterative solution of a class of nonsymmetric algebraic Riccati equations. This class includes a class of algebraic Riccati equations arising in transport theory. Using the special structure of the corresponding coefficient matrix and the theory of the M-matrices, the authors show that Newton's method and a class of basic fixed-point iterations can be used in order to find the minimal positive solution whenever such a solution exists. Moreover, the authors present an overall algorithm for the solution of nonsymmetric algebraic Riccati equations which is a combination of Newton's method and the basic fixed-point iteration. This algorithm has two nice features: (i) it can detect that an equation actually does not have a positive solution; (ii) it can detect and solve a singular or nearly singular problem efficiently.