技能报告:SPARSE SOLUTIONS FOR INVERSE PROBLEMS IN REPRODUCING KERNEL HILBERT SPACES

主页:官方365体育网投 编辑: 陈亮君    发布时间:2019-12-23    次点击

报告人:钱涛导员 澳门研讨企业

时间:2020年1月1日上午10:00-11:00

地点:365体育官网院楼数学部205实验室

联部人:李海绸导员


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.


报告人概况:钱涛,曾是澳门企业数学部组长和杰出导员,现任职澳门研讨企业。研讨方向:调和分析、复分析、Clifford分析、时频分析、信号处理。钱导员在全球著名技能刊物如Automatica、Math. Ann.、J. Funct. Anal.、Tran. Amer. Math, Soc.、IEEE Transactions on Automatic Control、IEEE Transactions on Image Processing等发表技能作文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技技能奖自然科技奖一等奖。


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