Fourier analysis of 2-point Hermite interpolatory subdivision schemes
Abstract
Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices.
Keywords
Hermite interpolation, curve fitting, subdivision, Fourier transform, distributions, convergence of infinite products, products of matrices, Paley-Wiener theorem, compact support.
Reference
Serge Dubuc, Daniel Lemire, and Jean-Louis Merrien, Fourier Analysis of 2-Point Hermite Interpolatory Subdivision Schemes, J. of Fourier An. and Appl., Volume 7, Issue 5, 2001, 532-552.
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BibTeX
@article{lemirejfaa2001,
author = {Serge Dubuc and Daniel Lemire and Jean-Louis Merrien},
title = {Fourier analysis of 2-point Hermite interpolatory subdivision schemes},
journal = {J. Fourier Anal.Appl.},
year = {2001},
volume = {7},
number = {5},
pages = {537-552},
url = {http://www.daniel-lemire.com/fr/documents/publications/ETRANSF31.pdf}
}
Authors
- Serge Dubuc: dubucs at dms.umontreal.ca
- Daniel Lemire: lemire at acm.org
- Jean-Louis Merrien: Jean-Louis.Merrien at insa-rennes.fr
