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

發布者:數學與信息學院發布時間:2019-12-23浏覽次數:10

报告人:钱涛教授 澳门科技大学

時間:2020年1月1日上午10:00-11:00

地點:數學與信息學院院樓數學系205實驗室



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.


報告人簡介:錢濤,曾是澳門大學數學系主任和傑出教授,現任職澳門科技大學。研究方向:調和分析、複分析、Clifford分析、時頻分析、信號處理。錢教授在國際著名學術刊物如Automatica、Math. Ann.、J. Funct. Anal.、Tran. Amer. Math, Soc.、IEEE Transactions on Automatic Control、IEEE Transactions on Image Processing等發表學術論文200余篇,擔任Math. Meth. Appli. Sci.、Complex Anal. Oper. Theory、Complex Varia. Ellip. Equations等SCI雜志副主編。獲第一屆澳門特別行政區科學技術獎自然科學獎一等獎。


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