Year: 2021
Author: Zuoqiang Shi, Bao Wang
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 865–879
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2104-m2020-0309
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 865–879
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Weighted nonlocal Laplacian Laplace-Beltrami operator Point cloud