数学科学学院学术报告[2024] 042号

(高水平大学建设系列报告922号)

报告题目: Interlacing Polynomial Method for Matrix Approximation

报告人：蔡剑锋 教授 （香港科技大学）

报告时间：2024年5月23日11：00-13：00

报告地点：汇星楼702                                                    

报告内容：Matrix approximation is a crucial technique in numerous research areas across science and engineering, such as machine learning, scientific computing, and signal processing. These fields often deal with high-dimensional datasets formatted as matrices, which necessitates the use of matrix approximation as a fundamental step in data processing. In this talk, we address the problem of approximating a data matrix by selecting a subset of its columns and/or rows either from the matrix itself or from other source matrices. We apply the method of interlacing polynomials, introduced by Marcus, Spielman, and Srivastava, to develop new deterministic algorithms and establish a theoretical limit on the minimum approximation error. Our algorithm is deterministic and operates in polynomial time. Additionally, our new bounds are asymptotically sharp in several challenging scenarios where current methods provide unnecessarily large error bounds.

报告人简历：

蔡剑锋，现任香港科技大学数学系教授。主要研究兴趣为信号，图像和数据的理论和算法基础。他在矩阵恢复，图像重构和成像算法等领域，取得了一系列开创性的科研成果。他关于矩阵补全的SVT算法对学术研究和实际应用产生重要影响，被广泛引用。他在2017年和2018年被评为全球高被引学者，学术文章总被引超13000次。

欢迎师生参加！

报告邀请人：李敏  

                                           数学科学学院

                         2024年5月20日