Fast Approximation on the 2-Sphere by Optimally Localized Approximate Identities

  • We introduce a method to construct approximate identities on the 2-sphere which have an optimal localization. This approach can be used to accelerate the calculations of approximations on the 2-sphere essentially with a comparably small increase of the error. The localization measure in the optimization problem includes a weight function which can be chosen under some constraints. For each choice of weight function existence and uniqueness of the optimal kernel are proved as well as the generation of an approximate identity in the bandlimited case. Moreover, the optimally localizing approximate identity for a certain weight function is calculated and numerically tested.

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Author:Volker Michel
URN (permanent link):urn:nbn:de:hbz:386-kluedo-14710
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (29)
Document Type:Preprint
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Technische Universität Kaiserslautern
Tag:Approximative Identität; Konvergenz; schnelle Approximation
approximate identity; convergence; fast approximation
GND-Keyword:Approximation ; Faltung; L2-Approximation ; Lokalisation; Multivariate Approximation ; Numerische Mathematik; Polynomapproximation ; Sphäre
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):41A35 Approximation by operators (in particular, by integral operators)
41A55 Approximate quadratures
42C25 Uniqueness and localization for orthogonal series
65D15 Algorithms for functional approximation
86-08 Computational methods

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