Improved spectral convergence rates for graph Laplacians on ε-graphs and k-NN graphs

• Published in: Applied and computational harmonic analysis Vol. 60; pp. 123 - 175
• Main Authors: Calder, Jeff, García Trillos, Nicolás
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2022
• Subjects: Discrete to continuum; Graph Laplacian; Laplace-Beltrami operator; Rates of convergence; Spectral convergence; Discrete to continuum; Graph Laplacian; Spectral convergence; Rates of convergence; Laplace-Beltrami operator

In this paper we improve the spectral convergence rates for graph-based approximations of weighted Laplace-Beltrami operators constructed from random data. We utilize regularity of the continuum eigenfunctions and strong pointwise consistency results to prove that spectral convergence rates are the...