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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 08 > No. 1


Multidimensional Lobachevsky Spline Integration on Scattered Data

PP: 145-151
Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi,
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.

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