中科院数学与系统科学研究院
数学研究所
动力系统研讨班报告
报告人：钱 涛 教授 (澳门大学)
题 目：The pre-orthogonal algorithm in reproducing kernel hilbert spaces
时 间：2019.12.01（星期日）, 10 :00-11:00
地 点：数学院南楼N902室
摘 要：A linear operator defined in the pattern of Riesz representation of a Hilbert space naturally inherits 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 the 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) 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.
