Graph approximations to the Laplacian spectra

DOI10.1142/S1793525320500442zbMath1494.58013arXiv1910.09224OpenAlexW2990379945MaRDI QIDQ5072111

Jinpeng Lu

Publication date: 25 April 2022

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.09224

zbMATH Keywords

discretizationmanifold with boundaryspectral convergencegraph Laplacianmetric-measure space

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

Approximations of the connection Laplacian spectra, Gelfand's inverse problem for the graph Laplacian, Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions

Cites Work

• Unnamed Item
• The Riemannian obstacle problem
• A variational approach to the consistency of spectral clustering
• A graph discretization of the Laplace-Beltrami operator
• Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator
• Spectral stability of metric-measure Laplacians
• Geometric Curvature Bounds in Riemannian Manifolds with Boundary
• Spectral convergence of the connection Laplacian from random samples
• Metric graph reconstruction from noisy data