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12月26日下午 03：00 - 04: 00
报告地点：正新楼209
校内联系人：李欣欣 xinxinli@jlu.edu.cn
报告摘要：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.
报告人简介：蔡剑锋是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。其关于矩阵补全的SVT算法对学术研究和实际应用产生重要影响，该研究文章谷歌被引次数超6000次。他关于图像重构的工作发表于被誉为数学四大期刊之一的Journal of the AMS。在2017年和2018年，蔡剑锋被评为全球高被引学者，学术文章总被引超14000次。
