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.
Digital Object Identifier (DOI)
Allasia, Giampietro; Cavoretto, Roberto; and De Rossi, Alessandra
"Multidimensional Lobachevsky Spline Integration on Scattered Data,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 18.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss1/18