Mathematics of Computation

Author(s): Daniela Rosca.
Journal: Math. Comp. 74 (2005), 1803-1829.
MSC (2000): Primary 42C40, 41A63; Secondary 41A15, 65D07, 41A17
Posted: March 14, 2005
Retrieve article in: PDF

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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Daniela Rosca
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
Email: rosca@math.uni-luebeck.de, Daniela.Rosca@math.utcluj.ro

DOI: 10.1090/S0025-5718-05-01754-0
PII: S 0025-5718(05)01754-0
Keywords: Wavelets, multivariate approximation, interpolation
Received by editor(s): October 3, 2003
Received by editor(s) in revised form: April 12, 2004
Posted: March 14, 2005
Additional Notes: Research supported by the EU Research Training Network MINGLE, HPRN-CT-1999-00117.
Copyright of article: Copyright 2005, American Mathematical Society

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