For large-scale discrete-time algebraic Riccati equations (DAREs) with high-rank nonlinear and constant terms, the stabilizing solutions are no longer numerically low-rank, resulting in the obstacle in the computation and storage. However, in some proper control problems such as power systems, the potential structure of the state matrix -- banded-plus-low-rank, might make the large-scale computation essentially workable. In this paper, a factorized structure-preserving doubling algorithm (FSDA) is developed under the frame of the banded inverse of nonlinear and constant terms. The detailed iterations format, as well as a deflation process of FSDA, are analyzed in detail. A partial truncation and compression technique is introduced to shrink the dimension of columns of low-rank factors as much as possible. The computation of residual, together with the termination condition of the structured version, is also redesigned.

翻译：对于具有高度非线性和恒定条件的大型离散代数-代数-里卡蒂方程式(DAREs),稳定化解决方案不再在数字上低,从而在计算和储存方面造成障碍,然而,在一些适当的控制问题中,如电力系统,国家矩阵的潜在结构 -- -- 带宽-加低级,可能使大规模计算基本可行。在本文中,在带宽的非线性和恒定条件下,在带宽的非线性和恒定条件框架下,开发了一种因子化结构维护结构的双重算法(FSDA),详细分析了详细的迭代格式以及FSDA通缩过程。引入了部分脱轨和压缩技术,以尽可能缩小低级因素柱子的尺寸。还重新设计了剩余值的计算以及结构化版本的终止条件。