Given a Riemannian manifold X with Riemannian measure μ and positive weights {ω_j}, j=1,...,N, we study the conditions under which there exist points {x_j}, j=1,...,N in X so that a cubature formula of the form ∫P dμ=∑ω_jP(x_j) holds for all polynomials P of order less than or equal to L. The problem is studied for diffusion polynomials (linear combinations of eigenfunctions of the Laplace–Beltrami operator) in the context of abstract Riemannian manifolds and for algebraic polynomials in the context of algebraic manifolds in R^n.

(2021). Asymptotically optimal cubature formulas on manifolds for prefixed weights [journal article - articolo]. In JOURNAL OF APPROXIMATION THEORY. Retrieved from http://hdl.handle.net/10446/188998

Asymptotically optimal cubature formulas on manifolds for prefixed weights

Gariboldi, Bianca;Gigante, Giacomo;
2021-01-01

Abstract

Given a Riemannian manifold X with Riemannian measure μ and positive weights {ω_j}, j=1,...,N, we study the conditions under which there exist points {x_j}, j=1,...,N in X so that a cubature formula of the form ∫P dμ=∑ω_jP(x_j) holds for all polynomials P of order less than or equal to L. The problem is studied for diffusion polynomials (linear combinations of eigenfunctions of the Laplace–Beltrami operator) in the context of abstract Riemannian manifolds and for algebraic polynomials in the context of algebraic manifolds in R^n.
articolo
2021
Ehler, Martin; Etayo, Ujué; Gariboldi, Bianca Maria; Gigante, Giacomo; Peter, Thomas
(2021). Asymptotically optimal cubature formulas on manifolds for prefixed weights [journal article - articolo]. In JOURNAL OF APPROXIMATION THEORY. Retrieved from http://hdl.handle.net/10446/188998
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/188998
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