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

TL;DR

This paper introduces a decoupled, structure-preserving doubling algorithm with truncation for efficiently solving large-scale algebraic Riccati equations with low-rank solutions, improving computational feasibility.

Contribution

It presents a novel decoupled form of the structure-preserving doubling algorithm with a truncation strategy for large-scale Riccati equations.

Findings

Efficiently solves large-scale algebraic Riccati equations.

Controls the rank of solutions via truncation.

Numerical examples confirm effectiveness.

Abstract

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.