Premium
Efficient reconstruction of functions on the sphere from scattered data
Author(s) -
Keiner Jens,
Kunis Stefan,
Potts Daniel
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700924
Subject(s) - spherical harmonics , focus (optics) , interpolation (computer graphics) , spin weighted spherical harmonics , fourier transform , basis function , spherical mean , function (biology) , zonal spherical harmonics , vector spherical harmonics , surface (topology) , mathematics , mathematical analysis , harmonics , physics , geometry , optics , classical mechanics , quantum mechanics , motion (physics) , voltage , evolutionary biology , biology
Motivated by the fact that most data collected over the surface of the earth is available at scattered nodes only, the least squares approximation and interpolation of such data has attracted much attention, see e.g. [1, 2, 5]. The most prominent approaches rely on so‐called zonal basis function methods [16] or on finite expansions into spherical harmonics [12, 14]. We focus on the latter, i.e., the use of spherical polynomials since these allow for the application of the fast spherical Fourier transform, see for example [8, 9] and the references therein. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)