Representing and analyzing scattered data on spheres
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.42024
publication date: 2002-08-14T00:00:00Z
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 86-08
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 1645831
zbMATH Keywords: scattered data approximation on spheres
zbMATH Keywords: geophysical data
zbMATH Keywords: spherical basis function
zbMATH Keywords: interpolation on spheres
zbMATH Keywords: multilevel interpolation
zbMATH Keywords: quadrature methods
zbMATH Keywords: spherical basis functions
zbMATH Keywords: spherical wavelet schemes
author: H. N. Mhaskar
author: F. J. Narcowich
author: J. D. Ward
MaRDI profile type: Publication
title: Representing and analyzing scattered data on spheres
review text: In this interesting survey article, the authors discuss recent progress in the representation and analysis of scattered data on the unit sphere \(S^q\) of \(\mathbb{R}^{q+1}\). This research is mainly motivated by the representation and analysis of geophysical or meteorological data collected over the surface of the earth via satellites or ground stations. First, the interpolation and approximation of scattered data on \(S^q\) is discussed. These methods involve spherical basis functions. The analysis of scattered data on \(S^q\) is based on spherical wavelet schemes. Localization and uncertainty principles on \(S^q\) are discussed, too. A brief introduction to multilevel interpolation is given. In both the representation and analysis of scattered data on \(S^q\), efficient computations of Fourier coefficients and convolutions are needed. Therefore various numerical schemes are reviewed. The authors close by discussing quadrature methods, which arise in many of the spherical wavelet schemes as well as interpolation methods.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00017].
reviewed by: Manfred Tasche
description: scientific article; zbMATH DE number 1645831