Title: Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations
We consider the numerical solution of large-scale M-matrix algebraic Riccati equations (MAREs) 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 novel triplet representations for the small M-matrix kernels in a highly accurate doubling algorithm. With these triplet representations, we develop a highly accurate doubling algorithm, named dADDA, for large-scale MAREs with low-rank structures, where the GTH-like algorithm is applied for solving the associated linear systems. Illustrative numerical examples will be presented on the efficiency of our algorithm.