Numerical methods for a quadratic matrix equation with a nonsingular M-matrix

We consider numerical solution of a quadratic matrix equation associated with a nonsingular M-matrix (M-QME), which arises in study of noisy Wiener-Hopf problems for Markov chain. We first transform the M-QME to a nonsymmetric algebraic Riccati equation (NARE) of special form, and then solve this special NARE by fixed-point iteration. Theoretical analysis and numerical experiments show that our method is effective and efficient.