梁鑫 研究员（清华大学丘成桐数学科学中心）
报告时间：2022年11月16号 9:30-10:30
腾讯会议： 634-964-412
报告题目： The intrinsic Toeplitz structure and its applications in algebraic Riccati equations
摘要：In this talk we derive a Toeplitz-structured closed form of the unique positive semi-definite stabilizing solution for the discrete-time algebraic Riccati equations, especially for the case that the state matrix is not stable. Based on the found form and fast Fourier transform, we propose a new algorithm for solving both discrete-time and continuous-time large-scale algebraic Riccati equations with low-rank structure. It works without unnecessary assumptions, complicated shift selection strategies, 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. This is a joint work with Zhen-Chen Guo.
邀请人： 张雷洪