Multidimensional Lobachevsky Spline Integration on Scattered Data

Authors

Giampietro Allasia, Department of Mathematics “G. Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Roberto Cavoretto
Alessandra De Rossi

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

N/A

Digital Object Identifier (DOI)

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

Recommended Citation

Allasia, Giampietro; Cavoretto, Roberto; and De Rossi, Alessandra (2014) "Multidimensional Lobachevsky Spline Integration on Scattered Data," Applied Mathematics & Information Sciences: Vol. 08: Iss. 1, Article 18.
DOI: http://dx.doi.org/10.18576/amis/080118
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss1/18