Computation with wavelets in higher dimensions
type: Item
instance of: scholarly article
title: Computation with wavelets in higher dimensions
zbMATH Open document ID: 0907.42023
author: Jan-Olov Strömberg
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/230758
full work available at URL: Stromberg.MAN.html
review text: Summary: In dimension \(d\), a lattice grid of size \(N\) has \(N^d\) points. The representation of a function by, for instance, splines or the so-called non-standard wavelets with error \(\varepsilon\) would require \(O(\varepsilon^{-ad})\) lattice point values (resp. wavelet coefficients), for some positive \(a\) depending on the spline order (resp. the properties of the wavelet). Unless \(d\) is very small, we easily will get a data set that is larger than a computer in practice can handle, even for very moderate choices of \(N\) or \(\varepsilon\). I discuss how to organize the wavelets so that functions can be represented with \[ O((\log(1/\varepsilon))^{a(d- 1)}\varepsilon^{- a}) \] coefficients. Using wavelet packets, the number of coefficients may be further reduced.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 1184390
zbMATH Keywords: higher dimensions
zbMATH Keywords: wavelets
zbMATH Keywords: lattice point values
zbMATH Keywords: wavelet coefficients
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1184390