Numerical integration on graphs: Where to sample and how to weigh

DOI10.1090/mcom/3515zbMath1437.05143arXiv1803.06989OpenAlexW2996020520WikidataQ111858760 ScholiaQ111858760MaRDI QIDQ4960080

Stefan Steinerberger, George C. Linderman

Publication date: 8 April 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.06989

zbMATH Keywords

samplingpackingheat kernelgraph Laplacian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Numerical quadrature and cubature formulas (65D32)

Related Items (10)

Sequences of well-distributed vertices on graphs and spectral bounds on optimal transport ⋮ Graph signal sampling and interpolation based on clusters and averages ⋮ Quadratures over graphs via the Frank-Wolfe method and its variant ⋮ Graph signal interpolation with positive definite graph basis functions ⋮ Overview of the topical collection: harmonic analysis on combinatorial graphs ⋮ Sums of distances on graphs and embeddings into Euclidean space ⋮ Graphical designs and gale duality ⋮ A low discrepancy sequence on graphs ⋮ Codes, cubes, and graphical designs ⋮ Quadrature points via heat kernel repulsion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Half sampling on bipartite graphs
• Sequences, discrepancies and applications
• Interpolating splines on graphs for data science applications
• The crystallization conjecture: a review
• Spherical codes and designs
• Sampling of Paley-Wiener functions on stratified groups
• Multiscale data sampling and function extension
• Quadrature points via heat kernel repulsion
• Distributing many points on spheres: minimal energy and designs
• The Stolarsky principle and energy optimization on the sphere
• Shannon sampling and weak Weyl's law on compact Riemannian manifolds
• From graph to manifold Laplacian: the convergence rate
• Sampling in Paley-Wiener spaces on combinatorial graphs
• A sampling theorem on homogeneous manifolds
• Local-Set-Based Graph Signal Reconstruction
• Eigenvalues of Laplacians on a Closed Riemannian Manifold and Its Nets
• Cubature Formulas and Discrete Fourier Transform on Compact Manifolds
• Clustering with t-SNE, Provably
• Spectral Limitations of Quadrature Rules and Generalized Spherical Designs
• Generalized designs on graphs: Sampling, spectra, symmetries
• Sums of Distances Between Points on a Sphere. II
• Poincaré and Plancherel--Polya Inequalities in Harmonic Analysis on Weighted Combinatorial Graphs

This page was built for publication: Numerical integration on graphs: Where to sample and how to weigh