CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

查看全文 作　　者：Zuoqiang [1]Shi;Bao [2]Wang 机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;[2]Department of Mathematics,University of Utah,Salt Lake City,UT 84112,USA 出　　处：《Journal of Computational Mathematics》索引2021年第39卷第6期,共15页 基　　金：Research supported by NSFC Grant 12071244;NSF DMS-1924935. 摘　　要：We analyze the convergence of the weighted nonlocal Laplacian(WNLL)on the high dimensional randomly distributed point cloud.Our analysis reveals the importance of the scaling weight,µ∼|P|/|S|with|P|and|S|being the number of entire and labeled data,respectively,in WNLL.The established result gives a theoretical foundation of the WNLL for high dimensional data interpolation. 关 键 词：Weighted nonlocal Laplacian Laplace-Beltrami operator Point cloud Highdimensional interpolation