Interpolating polynomial wavelets on \([-1,1]\)
type: Item
instance of: scholarly article
title: Interpolating polynomial wavelets on \([-1,1]\)
zbMATH Open document ID: 1071.65192
published in: Advances in Computational Mathematics
publication date: 2005-05-20T00:00:00Z
review text: The authors use a system of orthogonal polynomials with respect to the four Chebyshev weights, \(1/\sqrt(1-x^2)\), \(\sqrt(1-x^2)\), \(\sqrt{[(1-x)/(1+x)]}\) and \(\sqrt{[(1+x)/(1-x)]}\), with positive leading coefficients and Darboux kernels to construct four interpolating scaling functions and interpolating wavelets with a multiresolution structure. These wavelets, based on de la Vallée Poussin interpolation are more localized and give better approximation in the uniform weighted norm than polynomial wavelets based on Lagrange interpolation. However, the matrices involved in the two-scale relations are not orthogonal. The structure of these matrices is studied in detail: the elements of the inverse matrices are explicitly known and the computation of matrix-vector products can be performed by means of fast discrete cosine and sine transforms.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 2170080
zbMATH Keywords: polynomial wavelets
zbMATH Keywords: de la Vallée Poussin mean
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: fast discrete cosine and sine transforms
zbMATH Keywords: interpolating scaling functions
zbMATH Keywords: interpolating wavelets
zbMATH Keywords: multiresolution
author: M. R. Capobianco
author: Woula Themistoclakis
MaRDI profile type: Publication
full work available at URL: s10444-004-1828-2
OpenAlex ID: W2065868483
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DOI: 10.1007/S10444-004-1828-2
description: scientific article; zbMATH DE number 2170080