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Mathematics of Computation

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Locally supported rational spline wavelets on a sphere

Author: Daniela Roşca
Journal: Math. Comp. 74 (2005), 1803-1829
MSC (2000): Primary 42C40, 41A63; Secondary 41A15, 65D07, 41A17
Published electronically: March 14, 2005
MathSciNet review: 2164098
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Abstract: In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant associated to a given triangulation and study the approximation error. Some numerical examples are given to illustrate the efficiency of our wavelets.

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Additional Information

Daniela Roşca
Affiliation: Institute of Mathematics, University of Lübeck, Wallstrasse 40, Lübeck 23560, Germany
Address at time of publication: Department of Mathematics, Technical University of Cluj-Napoca, str. Daicoviciu 15, Cluj-Napoca 400020, Romania

Keywords: Wavelets, multivariate approximation, interpolation
Received by editor(s): October 3, 2003
Received by editor(s) in revised form: April 12, 2004
Published electronically: March 14, 2005
Additional Notes: Research supported by the EU Research Training Network MINGLE, HPRN-CT-1999-00117.
Article copyright: © Copyright 2005 American Mathematical Society