Ten lectures on wavelets
Error bounds for a convexity-preserving interpolation and its limit function
Journal of Computational and Applied Mathematics
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Tight numerical bounds for digital terrain modeling by interpolatory subdivision schemes
Mathematics and Computers in Simulation
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It is known that a multiresolution scheme without control on the infinity norm can produce numerical artifacts. This work is intended to provide explicit error bounds for the reconstruction process associated with the interpolating wavelets introduced by Donoho [D. Donoho, Interpolating Wavelet Transforms, Preprint, Department of Statistics, Stanford University, 1992]. The stability constants related to the interpolatory wavelets defined by the use of the Daubechies filters [I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992], also called the Deslaurier-Dubuc wavelets, are tabulated. Our study present two important facts: The first is that the obtained stability constants are much better approximated than those given by other approaches motivated by [S. Amat, J. Liandrat, On the stability of the PPH multiresolution algorithm, Appl. Comp. Harmon. Anal. 18 (2005) 198-206] and the second is that our analysis uses basic rules easily understood by a wide part of the scientific community interested in this kind of explicit numerical results.