Locally supported rational spline wavelets on a sphere

Author:
Daniela Rosca

Journal:
Math. Comp. **74** (2005), 1803-1829

MSC (2000):
Primary 42C40, 41A63; Secondary 41A15, 65D07, 41A17

DOI:
https://doi.org/10.1090/S0025-5718-05-01754-0

Published electronically:
March 14, 2005

MathSciNet review:
2164098

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 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:
https://doi.org/10.1090/S0025-5718-05-01754-0

Keywords:
Wavelets,
multivariate approximation,
interpolation

Received by editor(s):
October 3, 2003

Received by editor(s) in revised form:
April 12, 2004

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