Seminars on Numerical algebra, Optimization and Data Sciences：The intrinsic Toeplitz structure and its applications in algebraic Riccati equations

：梁鑫（清华大学）
：2022-12-08 10:00
：腾讯会议ID：334-129-008（无密码）

报告人：梁鑫（清华大学）

时  间：12月8日上午10:00-11:30

地  点：腾讯会议ID：334-129-008（无密码）

内容摘要:

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.

个人简介：

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；随后在德国马克斯普朗克复杂技术系统动力学研究所，新竹交通大学应用数学系，及美国德克萨斯大学阿灵顿分校数学系做博士后或访问学者；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；目前已在SIAM J. Matrix Anal. Appl.，IMA J. Numer. Anal.，等期刊发表论文多篇，主持国家自然科学青年基金。

 

联系人：杜魁