Lobachevsky spline functions and interpolation to scattered data

Autor:	Alessandra De Rossi, Giampietro Allasia, Roberto Cavoretto
Rok vydání:	2013
Předmět:	Box spline Applied Mathematics Gaussian Mathematical analysis Probabilistic logic Univariate Probability density function Computational Mathematics Spline (mathematics) symbols.namesake symbols Spline interpolation Mathematics Bochner's theorem
Zdroj:	Computational and Applied Mathematics. 32:71-87
ISSN:	1807-0302 0101-8205
DOI:	10.1007/s40314-013-0011-0
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c72df58f0654ae0bba5e6dc542b5c15 https://doi.org/10.1007/s40314-013-0011-0 Zobrazit plný text záznamu Full text from SpringerLink