A graph discretization of the Laplace-Beltrami operator

Dmitri Burago; Sergei Ivanov; Yaroslav Kurylev

arxiv: 1301.2222 · v4 · pith:J74NL4Z5new · submitted 2013-01-10 · 🧮 math.AP · math.DG· math.SP

A graph discretization of the Laplace-Beltrami operator

Dmitri Burago , Sergei Ivanov , Yaroslav Kurylev This is my paper

classification 🧮 math.AP math.DGmath.SP

keywords graphoperatoreigenvalueslaplace-beltramiapproximateddiscretizationeigenfunctionseigenvectors

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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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A graph discretization of the Laplace-Beltrami operator

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