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Author Country (or Countries)

Italy

Abstract

This paper deals with the topic of numerical integration on scattered data in Rd, d ≤10, by a class of spline functions, called Lobachevsky splines. Precisely, we propose new integration formulas based on Lobachevsky spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate integrals. Theoretically, Lobachevsky spline integration formulas have meaning for any d ∈ N, but numerical results appear quite satisfactory for d ≤ 10, showing good accuracy and stability. Some comparisons are given with radial Gaussian integration formulas and a quasi-Monte Carlo method using Halton data points sets.

Suggested Reviewers

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Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/080118

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