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arXiv 2011.014942020-11-03math.NAcs.NA

Decoupled Structure-Preserving Doubling Algorithm with Truncation for Large-Scale Algebraic Riccati Equations

Zhen-Chen Guo, Eric King-Wah Chu, Xin Liang, Wen-Wei Lin

备注：: 32 pages, 4 figures, 2 tables

英文摘要：

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.

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