In this paper we propose a new algorithm for solving large-scale algebraic Riccati equations with low-rank structure. The algorithm is based on the found Toeplitz-structured closed form of the stabilizing solution and the fast Fourier transform. It works without unnecessary assumptions, shift selection trategies, or matrix calculations of the cubic order with respect to the problem scale. Numerical examples are given to illustrate its features. Besides, we show that it is theoretically equivalent to several algorithms existing in the literature in the sense that they all produce the same sequence under the same parameter setting.

翻译：在本文中,我们提出一个新的算法,用于解决结构结构低的大型代数里卡蒂方程式。算法基于找到的Teplitz结构封闭式的稳定解决方案和快速Fourier变异。它没有不必要的假设、转移选择策略或对问题规模的立方顺序矩阵计算。提供了数字示例来说明其特征。此外,我们表明,它理论上等同于文献中存在的几种算法,即它们在相同的参数设置下产生相同的序列。