报告题目 Title: Kernel-based Regularity Estimation--Nested Data

报告人 Speaker: Leevan Ling

报告人所在单位 Affiliation: Hong Kong Baptist University

时间 Time: 2025-12-29 16:00-17:00

地点 Venue: Room 2001, Guanghua Eastern Main Tower (Handan Campus)

报告摘要 Abstract: We study the same problem of estimating the local regularity of an unknown function $f : \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$ from scattered samples $(X, f(X))$, but from a different theoretical standpoint. Building on Sobolev-space reproducing kernels, we establish a rigorous correspondence between the convergence rate of kernel approximants and the underlying Sobolev smoothness of the target function. The analysis develops a distinct framework based on newly proven Bernstein-type inverse inequalities for kernel trial spaces, which lead to an improved inverse theorem for kernel interpolation on bounded domains. In contrast to earlier inverse formulations requiring convergence over all quasi-uniform node sets, the improved theory proves that smoothness can be recovered from one carefully constructed nested sequence of point sets. This theoretical advance underpins quantitative regularity estimation in kernel-based approximation and numerical experiments in various settings highlight the effectiveness of the proposed algorithm.

个人简介 Bio: Leevan Ling is Professor and Head of the Department of Mathematics at Hong Kong Baptist University (HKBU). He obtained his Ph.D. from Simon Fraser University and has been at HKBU since 2006. His research focuses on meshfree methods, radial basis functions, partial differential equations, and numerical analysis, with over 100 publications in these areas. Prof. Ling has received several research grants from the Hong Kong Research Grant Council and has played key roles in organizing international conferences on scientific computing and PDEs. He is actively involved in academic leadership, program development, and collaborative research in computational mathematics.

海报 Poster: Leevan Ling 学术报告.jpg