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arXiv · 2011.00471

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

Zhen-Chen Guo·Eric King-wah Chu·Xin Liang
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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.

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Zhen-Chen Guo, Eric King-wah Chu, Xin Liang. 2020-11-01. Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations. https://arxiv.org/abs/2011.00471

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