Tensor Spherical Harmonics and Tensor Spherical Splines

  • In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor fields are investigated and a decomposition formula is described. Tensor spherical harmonics are introduced as eigenfunctions of a tensorial analogon to the Beltrami operator and discussed in detail. Based on these preliminaries, a spline interpolation process is described and error estimates are presented. Furthermore, some relations between the spline basis functions and the theory of radial basis functions are developed.

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Author:Willi Freeden, T. Gervens, Michael Schreiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-6940
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (88)
Document Type:Preprint
Language of publication:English
Year of Completion:1993
Year of Publication:1993
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Source:Manuscripta Geodaetica, 19, 70-100 (1994)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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