报告题目：The Haar Wavelet Analysis of Matrices and its Applications

报告人：施锡泉（美国特拉华州立大学（Delaware State University）终身教授）

报告时间：2021年7月8日8时30分

邀请人：钱江

报告摘要：It is well known that Fourier analysis or wavelet analysis is a very powerful and useful tool for a function since they convert time-domain problems into frequency-domain problems. Does it has similar tools for a matrix? By pairing a matrix to a piecewise function, a Haar-like wavelet is used to set up a similar tool for matrix analyzing, resulting in new methods for matrix approximation and orthogonal decomposition. By using our method, one can approximate a matrix by matrices with different orders. Our method also results in a new matrix orthogonal decomposition, reproducing Haar transformation for matrices with orders of powers of two. The computational complexity of the new orthogonal decomposition is linear. In addition, when the method is applied to k-means clustering, one can obtain that k-means clustering can be equivalent converted to the problem of finding a best approximation solution of a function. In fact, the results in this paper could be applied to any matrix related problems. In addition, one can also employee other wavelet transformations and Fourier transformation to obtain similar results.

报告人简介：施锡泉，现任特拉华州立大学（Delaware State University）终身教授。曾于1992年至2001年任职大连理工大学，历任副教授、教授和博士导师之职。获得荣誉包括：德国洪堡科研基金（Alexander von Humboldt-Stiftung）、霍英东高校青年教师研究基金、教育部 (原国家教委)科技进步二等奖，大连市十大杰出科技青年等。研究方向包括计算几何、多元样条、特殊函数等，已发表论文90余篇