  We consider the large scale nonsymmetric algebraic Riccati equation arising
in transport theory, where the $n\times n$ coefficient matrices $B, C$ are
symmetric and low-ranked and $A, E$ are rank one updates of nonsingular
diagonal matrices. By introducing a balancing strategy and setting appropriate
initial matrices carefully, we can simplify the large-scale
structure-preserving doubling algorithm (SDA\_ls) for this special equation. We
give modified large-scale structure-preserving doubling algorithm, which can
reduce the flop operations of original SDA\_ls by half. Numerical experiments
illustrate the effectiveness of our method.
