A graph discretization of the Laplace-Beltrami operator

Dmitri Burago; Sergei Ivanov; Yaroslav Kurylev

doi:10.4171/JST/83

A graph discretization of the Laplace-Beltrami operator

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

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 language	English (US)
Pages (from-to)	675-714
Number of pages	40
Journal	Journal of Spectral Theory
Volume	4
Issue number	4
DOIs	https://doi.org/10.4171/JST/83
State	Published - 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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10.4171/JST/83

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title = "A graph discretization of the Laplace-Beltrami operator",

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.",

author = "Dmitri Burago and Sergei Ivanov and Yaroslav Kurylev",

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year = "2014",

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T1 - A graph discretization of the Laplace-Beltrami operator

AU - Burago, Dmitri

AU - Ivanov, Sergei

AU - Kurylev, Yaroslav

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:84994065494

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EP - 714

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 4

ER -

A graph discretization of the Laplace-Beltrami operator

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All Science Journal Classification (ASJC) codes

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