学术报告:SPARSE SOLUTIONS FOR INVERSE PROBLEMS IN REPRODUCING KERNEL HILBERT SPACES

审核发布:数学与信息学院 来源单位及审核人: 发布时间:2019-12-23浏览次数:227

报告人:钱涛教授 澳门科技大学

时间:2020年1月1日上午10:00-11:00

地点:数学与信息学院院楼数学系205实验室



Abstract:A linear operator defined in the pattern of Riesz representation in a Hilbert space naturally introduces a reproducing kernel Hilbert space structure over the range space. The present study shows that such formulation of linear operators possesses a build-in mechanism of representing solutions of most important types of fundamental problems, viz., the identification of the range, the inverse problem, and the Moore-Penrose pseudo-inverse problem. This talk aims to spell out the connections of these problems and gives explicit representation formulas in the form of infinite series of the solutions. Apart from the basic basis method, the talk mainly proposes a pre-orthogonal adaptive Fourier decomposition (POAFD) method in contrast with the basis method. Optimality of the maximal selection principle of POAFD evidences that on the one-step-selection strategy the algorithm and its variations are indeed the most effective and offer practical and fast converging numerical solutions.


报告人简介:钱涛,曾是澳门大学数学系主任和杰出教授,现任职澳门科技大学。研究方向:调和分析、复分析、Clifford分析、时频分析、信号处理。钱教授在国际著名学术刊物如Automatica、Math. Ann.、J. Funct. Anal.、Tran. Amer. Math, Soc.、IEEE Transactions on Automatic Control、IEEE Transactions on Image Processing等发表学术论文200余篇,担任Math. Meth. Appli. Sci.、Complex Anal. Oper. Theory、Complex Varia. Ellip. Equations等SCI杂志副主编。获第一届澳门特别行政区科学技术奖自然科学奖一等奖。


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