Lobachevsky spline functions and interpolation to scattered data

• DOI: 10.1007/s40314-013-0011-0
• Publication Date: 2013-08-28T16:37:55Z
• Authors: Giampietro Allasia; Roberto Cavoretto; Alessandra De Rossi
• Keywords: 0101 mathematics; 01 natural sciences

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.