题目：Distributed uncertaintyquantification 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 theUniversity of Texas at Austin. He is currently a distinguished professor andformer associate dean of the School of Natural and Applied Sciences at MissouriState University. He has served on the editorial boards of severalinternationally renowned journals  and publishedmore than 60 articles in top international journals such as Foundation ofComputational Mathematics, IEEE Transactions on Neural Networks and LearningSystems, SIAM Journal on Scientific Computing, and SIAM Journal on NumericalAnalysis. He has been invited to visit universities in the UK, France, Germany,and domestic universities such as Fudan University, Zhejiang University, andSun Yat-sen University. 

摘要：For radial basis function (RBF) kernel interpolation ofscattered data, Schaback in 1995 proved that the attainable approximation errorand the condition number of the underlying interpolation matrix cannot be madesmall simultaneously. He referred to this finding as an ``uncertaintyrelation", an undesirable consequence of which is that RBF kernelinterpolation is susceptible to noisy data. In this paper, we propose and studya distributed interpolation method to manage and quantify the uncertaintybrought on by interpolating noisy spherical data of non-negligible magnitude.We also present numerical simulation results showing that our method ispractical and robust in handling noisy data from challenging computingenvironments.