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Multidimensional Lobachevsky Spline Integration on Scattered Data |
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PP: 145-151 |
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Author(s) |
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Giampietro Allasia,
Roberto Cavoretto,
Alessandra De Rossi,
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Abstract |
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| 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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