  We consider the numerical solution of large-scale M-matrix algebraic Riccati
equations with low-rank structures. We derive a new doubling iteration,
decoupling the four original iteration formulae in the alternating-directional
doubling algorithm. We prove that the kernels in the decoupled algorithm are
small M-matrices. Illumined by the highly accurate algorithm proposed by Xue
and Li in 2017, we construct the triplet representations for the small M-matrix
kernels in a highly accurate doubling algorithm. Illustrative numerical
examples will be presented on the efficiency of our algorithm.
