报告题目：The intrinsic Toeplitz structure and its applications in algebraic Riccati equations
时 间：2022年11月20日（星期日）下午2:30
地 点：腾讯会议（会议号：532-214-751）
主 办：数学与统计学院，福建省分析数学及应用重点实验室，福建省应用数学中心（福建师范大学），福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：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.
报告人简介：梁鑫，分别于2009年和2014年在北京大学数学科学学院获得理学学士和理学博士学位，自2018年起在清华大学丘成桐数学科学中心任助理教授，从事数值线性代数、矩阵分析等领域的研究。