Quadratic spline wavelets with arbitrary simple knots on the sphere

Authors:
El Bachir Ameur;Driss Sbibih
Affiliations:
Département de Mathématiques et Informatique, Université Mohammed I, Oujda, Morocco;Département de Mathématiques et Informatique, Université Mohammed I, Oujda, Morocco
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Year:
2004

Citing 6
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Abstract

In this paper, we extend the method for fitting functions on the sphere, described in Lyche and Schumaker (SIAM J. Sci. Comput. 22 (2) (2000) 724) to the case of nonuniform knots. We present a multiresolution method leading to -functions on the sphere, which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the tensor product decomposition and reconstruction algorithms in matrix forms which are convenient for the compression of surfaces. We give the different steps of computer implementation and finally we present a test example by using two knot sequences: a uniform one and a sequence of Chebyshev points.