Periodized Daubechies wavelets
Juan M. Restrepo,Gary K. Leaf,G. Schlossnagle +2 more
- 01 Mar 1996
TL;DR: In this paper, the analytical solution to inner products of periodized wavelets and their derivatives, known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators.
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Abstract: The properties of periodized Daubechies wavelets on [0,1] are detailed and counterparts which form a basis for L{sup 2}(R) Numerical examples illustrate the analytical estimates for convergence and demonstrated by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators The periodization of the connection coefficients in Galerkin schemes is presented in detail
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Citations
On the Use of Wavelets in Computational Combustion
Robert Prosser,RS Cant +1 more
TL;DR: In this paper, a spatial discretisation scheme using biorthogonal wavelets is presented and applied to a test problem involving flame propagation in a representative fuel?air mixture, in which the chemistry is treated using a standard four-step reduced reaction mechanism.
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An adaptive algorithm for compressible reacting flows using interpolating wavelets
Robert Prosser
- 01 Nov 2007
TL;DR: A wavelet-based method for the simulation of reacting flows on adaptive meshes is presented in this article, which is based on the removal of grid points whose wavelet coefficients are small with reference to some user-specified threshold.
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The theoretical development of wavelets in reacting flows
Robert Prosser,RS Cant +1 more
- 01 Nov 2000
TL;DR: In this paper, the authors focus on the simulation of turbulent reacting flows via recent developments in wavelet-based analyses and present a fast transform algorithm for interpolating wavelet transforms based on second-generation wavelets.
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•Posted Content
Empirical Wavelet-based Estimation for Non-linear Additive Regression Models
TL;DR: This paper proposes an estimator based on an orthogonal projection onto a multiresolution space using empirical wavelet coefficients that are fully data driven and achieves good convergence rates when the dimensionality of the problem is relatively low and the set of unknown functions is sufficiently smooth.
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Periodized Wavelet Packets on Bounded Subsets of $$\boldsymbol{\mathbb{R}}$$
N. Khanna,S. K. Kaushik,M. Pap +2 more
TL;DR: In this article, Daubechies periodized wavelet packets (DPWP) were studied and a necessary condition for it was given and an estimate for the approximation error related to DPWP was given.
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