A graph discretization of the Laplace-Beltrami operator

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

Original languageEnglish (US)
Pages (from-to)675-714
Number of pages40
JournalJournal of Spectral Theory
Volume4
Issue number4
DOIs
StatePublished - Jan 1 2014

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Proximity Graphs
Laplace-Beltrami Operator
Eigenvalues and Eigenfunctions
Eigenvalues and Eigenvectors
Laplace Operator
Weighted Graph
Riemannian Manifold
eigenvectors
eigenvalues
Discretization
Laplace transformation
operators
Graph in graph theory
proximity

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology

Cite this

Burago, Dmitri ; Ivanov, Sergei ; Kurylev, Yaroslav. / A graph discretization of the Laplace-Beltrami operator. In: Journal of Spectral Theory. 2014 ; Vol. 4, No. 4. pp. 675-714.
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A graph discretization of the Laplace-Beltrami operator. / Burago, Dmitri; Ivanov, Sergei; Kurylev, Yaroslav.

In: Journal of Spectral Theory, Vol. 4, No. 4, 01.01.2014, p. 675-714.

Research output: Contribution to journalArticle

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