The Orthogonal Polynomial Approximation in the Reproducing Kernel Hilbert Space
发布时间：2023年05月18日
浏览次数：2467
发布者: He Liu
主讲人： He Zhang(PKU)
活动时间： 从 2023-05-21 16:00 到 17:30
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
The reproducing kernel Hilbert space (RKHS) is a particular class of Hilbert space satisfying the reproducing property. All its elements yield similar properties to the corresponding kernel, e.g., regularity and decay rate. My talk will revisit the orthogonal polynomial approximation using an RKHS setup, including
1. construct kernels and RKHS via orthogonal polynomials,2. discuss the universality (denseness in the continuous function spaces) of the resulting RKHS,
3. study the approximation error, and
4. guide in choosing the hypothesis spaces for statistical learning problems.
My talk will briefly introduce the RKHS theory, including the famous Mercer's theorem, and show application examples in density function estimation and Polynomial Chaos expansion.
