Minimal energy spherical splines on Clough-Tocher triangulations for Hermite interpolation
type: Item
instance of: scholarly article
title: Minimal energy spherical splines on Clough-Tocher triangulations for Hermite interpolation
zbMATH Open document ID: 1251.65010
published in: Applied Numerical Mathematics
publication date: 2012-07-13T00:00:00Z
review text: The authors address the problem of Hermite interpolation, with a Hermite interpolating spherical spline, based on the Clough-Tocher triangular macro-elements problem which can be used in the estimation of the geo-potential near the surface of the Earth. The minimal energy interpolation method is used, the existence and uniqueness of the minimal energy spherical splines, satisfying Hermite interpolation conditions, being studied. It is proved that the approximation error of a given sufficiently smooth function by the minimal energy Hermite interpolating spline depends on the mesh size of the underlying triangulation cubically. Also, the equivalence between the energy functional minimizers related to different homogeneous extensions is shown in the sense that they all converge to the sampled functions, the order of convergence being independent of the extensions. Some numerical experiments are also done to complete the paper.
reviewed by: Nicoleta Breaz
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 6055242
zbMATH Keywords: Clough-Tocher macro-element
zbMATH Keywords: spherical Hermite interpolation
zbMATH Keywords: energy minimization
zbMATH Keywords: minimal energy spherical splines
zbMATH Keywords: Hermite interpolating spline
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
author: Victoria Baramidze
MaRDI profile type: Publication
full work available at URL: j.apnum.2011.06.008
OpenAlex ID: W2051275175
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DOI: 10.1016/J.APNUM.2011.06.008
description: scientific article; zbMATH DE number 6055242