Effects of a parameter on a nonsymmetric algebraic Riccati equation

In this paper, we are interested in a nonsymmetric algebraic Riccati equation arising in transport theory. The effects of a parameter α on the minimal positive solution X*(α) of this equation are studied. We show that X*(α) decreases in α only when α is close to one and X*(α) cannot attain its maximum for α ∈ [0, 1). A matrix lower bound and a matrix upper bound for X*(α) are also given.