TY - JOUR
T1 - Convergence of the Weighted Nonlocal Laplacian on Random Point Cloud
AU - Shi , Zuoqiang
AU - Wang , Bao
JO - Journal of Computational Mathematics
VL - 6
SP - 865
EP - 879
PY - 2021
DA - 2021/10
SN - 39
DO - http://doi.org/10.4208/jcm.2104-m2020-0309
UR - https://global-sci.org/intro/article_detail/jcm/19915.html
KW - Weighted nonlocal Laplacian, Laplace-Beltrami operator, Point cloud
KW - High-dimensional interpolation.
AB - <p style="text-align: justify;">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, $\mu \sim |P|/|S|$ 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.</p>