Multidimensional Lobachevsky Spline Integration on Scattered Data
Autor: | Giampietro Allasia, Roberto Cavoretto, Alessandra De Rossi |
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Rok vydání: | 2014 |
Předmět: |
Numerical Analysis
Mathematical optimization Applied Mathematics Univariate Computer Science Applications Numerical integration Spline (mathematics) Smoothing spline symbols.namesake Data point Computational Theory and Mathematics M-spline Gaussian integral symbols Applied mathematics Analysis Mathematics |
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 |
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