Multidimensional Lobachevsky Spline Integration on Scattered Data

Autor: Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi
Rok vydání: 2014
Předmět:
Zdroj: Applied Mathematics & Information Sciences. 8:145-151
ISSN: 2325-0399
1935-0090
DOI: 10.12785/amis/080118
Popis: This paper deals with the topic of numerical integration on scattered data in R d , 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 in tegrals. Theoretically, Lobachevsky spline integration formulas have meaning for any d 2 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.
Databáze: OpenAIRE