Spherical splines and interpolation on a sphere
type: Item
instance of: scholarly article
title: Spherical splines and interpolation on a sphere
zbMATH Open document ID: 0845.41008
published in: Computational Mathematics and Mathematical Physics
publication date: 1996-09-11T00:00:00Z
review text: The author considers certain functions on the unit sphere \(\Omega\) in \(\mathbb{R}^3\), denoted as spherical splines. Here, a spherical spline, associated with the ``knots'' \(\{x_j\}\), is a function \(s\) of the form \[ s(x) = Q(x) + \sum^N_{j =1} d_j G(x,x_j), \quad x \in \Omega, \] where \(Q\) is a spherical harmonic and \(G\) is a function of the form \[ G(x,y) = \sum^\infty_{k = 1} g_k P_k (xy), \] \(P_k\) being the \(k\)th Legendre polynomial. Moreover, the coefficients \(d_j\) are to be taken from a specific point set described in the paper. The author proves the unique solvability of a certain interpolation problem for these spherical splines, and shows that they have a minimum norm property w.r.t. all solutions of this interpolation problem.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 859632
zbMATH Keywords: spherical harmonics
zbMATH Keywords: minimum norm problem
zbMATH Keywords: spherical spline
author: A. B. Pevnyj
reviewed by: Guido Walz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 859632