论文标题
大规模代数riccati方程的截断，将结构的脱钩结构加倍算法
Decoupled Structure-Preserving Doubling Algorithm with Truncation for Large-Scale Algebraic Riccati Equations
论文作者
论文摘要
在\ emph {Guo等，Arxiv：2005.08288}中，我们提出了一种脱钩的结构构成二倍算法（DSDA）。该方法将原始的两到四个耦合递归分解，从而使其能够求解大规模的代数riccati方程和其他相关问题。在本文中，我们考虑了新型DSDA的数值计算，用于求解具有低级别结构的大规模连续时间代数riccati方程（从而具有数值低的溶液）。借助新的截断策略，控制了近似解决方案的等级。因此，可以有效地处理大规模问题。提出了说明性的数值示例，以证明和确认我们的主张。
In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recursions, enabling it to solve large-scale algebraic Riccati equations and other related problems. In this paper, we consider the numerical computations of the novel dSDA for solving large-scale continuous-time algebraic Riccati equations with low-rank structures (thus possessing numerically low-rank solutions). With the help of a new truncation strategy, the rank of the approximate solution is controlled. Consequently, large-scale problems can be treated efficiently. Illustrative numerical examples are presented to demonstrate and confirm our claims.
