内容簡介：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.

報告人：蔡劍鋒

報告人簡介：香港科技大學數學系教授，擁有豐富的學術背景和卓越的研究成果。他于2000年獲得複旦大學計算數學學士學位，2007年獲得香港中文大學數學博士學位。博士畢業後，蔡劍鋒曾在多所世界知名大學工作，包括新加坡國立大學（2007-2009）、美國洛杉矶加州大學（UCLA）（2009-2011）、美國愛荷華大學（University of Iowa）（2011-2015）和香港科技大學（2015-今）。2019年，他在香港科技大學數學系晉升為教授。蔡劍鋒的研究興趣主要集中在成像技術和數據科學中的算法和數學理論基礎。他在這些領域取得了一系列開創性的科研成果，發表了多篇高引用論文，并在2017年和2018年被評為全球高被引學者。蔡劍鋒目前擔任《Frontiers in Applied Mathematics and Statistics》雜志優化方向的主編和《Journal of Mathematical Imaging and Vision》的編委。

題目二：Phase Retrieval and Blind Deconvolution Theory under Random Mask Assumption

内容簡介：Instead of traditional Gaussian random measurements, we focus on the phase retrieval problem under masked Fourier measurements. It is one of the phase retrieval settings which is realizable in real applications. We discuss some truncated Wirtinger flow algorithm and improve the sampling complexity. Furthermore, we also analyze the blind deconvolution problem with modulated inputs. It is a challenging problem as both the blur kernel and the input signal are not known. When the signal is sparse and the blur kernel is short-supported, we present an algorithm with the sampling complexity smaller than nuclear norm minimization and least square method.

報告人：夏羽

報告人簡介：杭州師範大學數學學院副教授，畢業于浙江大學數學系（導師: 李松教授），主要從事信号圖像處理中的數學理論和算法研究。現階段在應用數學及數學與信息交叉領域發表一系列學術論文, 包括 Applied and Computational Harmonic Analysis, Inverse Problems, IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing等。主持國家自然科學基金項目兩項。

題目三：Randomized Iterative Methods: Acceleration and Applications

内容簡介：Randomized iterative methods, such as the randomized Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems.  In this talk, we will explore the most recent advancements in the field of randomized iterative methods. This includes the exploration of the randomized Douglas-Rachford method, the adaptive parameter selection strategy for heavy ball momentum, and the application of randomized iterative methods to generalized absolute value equations.

報告人：謝家新

報告人簡介：北京航空航天大學副教授，博士生導師，2017年獲湖南大學計算數學博士學位，随後進入中國科學院數學與系統科學研究院從事博士後研究，2019年入職北京航空航天大學數學科學學院。研究興趣為數據科學中的數學問題，特别是随機疊代法和矩陣子集選擇等問題。已在SIMAX, SIOPT, IJM, JCM, COAP等期刊發表論文多篇。現為中國運籌學會算法軟件及應用分會理事，中國運籌學會數學規劃分會青年理事。

時  間：2024年12月1日（周日）下午16：00開始

地  點：太阳集团app首页番禺校區圖書館617會議室

熱烈歡迎廣大師生參加!

太阳集团1088vip

2024年11月28日