CONVERGENCE OF LAPLACIAN SPECTR A FROM R ANDOM SA MPLES  

作　　者：Wenqi Tao Zuoqiang Shi 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China

出　　处：《Journal of Computational Mathematics》2020年第6期952-984,共33页计算数学（英文）

基　　金：This research was supported by NSFC Grant 11671005.

摘　　要：Eigenvectors and eigenvalues of discrete Laplacians are often used for manifold learning and nonlinear dimensionality reduction.Graph Laplacian is one widely used discrete laplacian on point cloud.It was previously proved by Belkin and Niyogithat the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled independently from the uniform distribution over the manifold.Recently,we introduced Point Integral method(PIM)to solve elliptic equations and corresponding eigenvalue problem on point clouds.In this paper,we prove that the eigenvectors and eigenvalues obtained by PIM converge in the limit of infinitely many random samples.Moreover,estimation of the convergence rate is also given.

关 键 词：Graph Laplacian Laplacian spectra Random samples Spectral convergence 

分 类 号：O17[理学—数学]