Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev
Abstract
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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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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.
Key concepts: Laplace–Beltrami operator, Mathematics, Laplace operator, Eigenvalues and eigenvectors, Eigenfunction, Riemannian manifold, Operator (biology), Graph