Lobachevsky spline functions and interpolation to scattered data

被引：0
作者：
Giampietro Allasia
Roberto Cavoretto
Alessandra De Rossi
机构：
[1] University of Turin,Department of Mathematics “G. Peano”
来源：
Computational and Applied Mathematics | 2013年 / 32卷
关键词：
Spline functions; Probability limit theorems; Bochner’s theorem; Positive-definite basis functions; Univariate- and multivariate-scattered interpolation; 65D05; 65D07; 60F05;
D O I：
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学科分类号：
摘要：
To investigate errors in astronomical measurements Lobachevsky introduced in 1842 an infinite sequence of univariate spline functions with equally spaced knots, whom classic B-splines are directly connected to. A remarkable property is the convergence of the sequences of the Lobachevsky splines and of their derivatives to the normal (or Gaussian) density function and to its derivatives, respectively. This fact suggests to consider Lobachevsky splines for applications to univariate and multivariate scattered interpolation. First, this paper attempts to gather the most significant properties of Lobachevsky splines, generally sparse in the literature, maintaining for convenience a probabilistic setting. Then, applications to interpolation are discussed and numerical experiments, which show an interesting approximation performance, are given.
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页码：71 / 87
页数：16
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共 24 条
[1]  
Allasia G(2011)Scattered and track data interpolation using an efficient strip searching procedure Appl Math Comput 217 5949-5966
[2]  
Besenghi R(2012)A class of spline functions for landmark-based image registration Math Methods Appl Sci 35 923-934
[3]  
Cavoretto R(2008)On the convergence of derivatives of B-splines to derivatives of the Gaussian functions Comput Appl Math 27 79-92
[4]  
De Rossi A(2010)Fast and accurate interpolation of large scattered data sets on the sphere J Comput Appl Math 234 1505-1521
[5]  
Allasia G(2012)Spherical interpolation using the partition of unity method: an efficient and flexible algorithm Appl Math Lett 25 1251-1256
[6]  
Cavoretto R(1972)The numerical evaluation of B-splines J Inst Math Appl 10 134-149
[7]  
De Rossi A(2009)Approximation of Gaussian by scaling functions and biorthogonal scaling polynomials Bull Malays Math Sci Soc 32 261-282
[8]  
Brinks R(1842)Probabilité des résultats moyens tirés d’observations répetées J Reine Angew Math 24 164-170
[9]  
Cavoretto R(1946)Contributions to the problem of approximation of equidistant data by analytic functions Q Appl Math 4 45-99
[10]  
De Rossi A(1931)Su di una variabile casuale connessa con un notevole tipo di partizioni di un numero intero Giorn Istit Italiano Attuari 2 455-468
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