论文标题
对于大型M-Matrix代数riccati方程的高度精确的解耦合算法
Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations
论文作者
论文摘要
我们考虑具有低级别结构的大规模M-Matrix代数riccati方程的数值解。我们得出了一种新的双重迭代，将四个原始迭代公式解耦，以交替的方向加倍算法。我们证明，解耦算法中的核是小M型。由Xue和Li在2017年提出的高度精确算法阐明，我们在高度准确的加倍算法中构建了小M-Matrix内核的三重态表示。说明性的数值示例将以我们的算法效率介绍。
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.
