## Spherical panel clustering and its numerical aspects

• In modern approximation methods linear combinations in terms of (space localizing) radial basis functions play an essential role. Areas of application are numerical integration formulas on the uni sphere omega corresponding to prescribed nodes, spherical spline interpolation, and spherical wavelet approximation. the evaluation of such a linear combination is a time consuming task, since a certain number of summations, multiplications and the calculation of scalar products are required. This paper presents a generalization of the panel clustering method in a spherical setup. The economy and efficiency of panel clustering is demonstrated for three fields of interest, namely upward continuation of the earth's gravitational potential, geoid computation by spherical splines and wavelet reconstruction of the gravitational potential.

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Author: Willi Freeden, Oliver Glockner, Michael Schreiner urn:nbn:de:hbz:386-kluedo-5888 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (183) Preprint English 1997 1997 Technische Universität Kaiserslautern 2000/04/03 Panel clustering ; numerical integration ; spline and wavelet based determination of the geoid and the gravitational potential Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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