Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations

Abstract

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.

24 pages, 6 figures, 2 tables

References in corpus (1)

• A decoupled form of the structure-preserving doubling algorithm with low-rank structures