题目：Distributed uncertainty quantification for scattered data interpolation on spheres

汇报人：孙兴平

会议时间：2024年5月17日14:00-14:50

地点：综合楼644会议室

报告人简介：Xingping Sun got his Ph.D. of mathematics from the University of Texas at Austin. He is currently a distinguished professor and former associate dean of the School of Natural and Applied Sciences at Missouri State University. He has served on the editorial boards of several internationally renowned journals  and published more than 60 articles in top international journals such as Foundation of Computational Mathematics, IEEE Transactions on Neural Networks and Learning Systems, SIAM Journal on Scientific Computing, and SIAM Journal on Numerical Analysis. He has been invited to visit universities in the UK, France, Germany, and domestic universities such as Fudan University, Zhejiang University, and Sun Yat-sen University. 

摘要：For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an ``uncertainty relation", an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in handling noisy data from challenging computing environments.