Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions

Authors:
Daan Huybrechs;Stefan Vandewalle
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Leuven B-3001, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Leuven B-3001, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 6
Cited 2

Numerical analysis: 4th ed

Numerical analysis: 4th ed
Using the refinement equation for evaluating integrals of wavelets

SIAM Journal on Numerical Analysis
Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions

SIAM Journal on Numerical Analysis
Integral equations: theory and numerical treatment

Integral equations: theory and numerical treatment
A note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel

Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

A two-dimensional wavelet-packet transform for matrix compression of integral equations with highly oscillatory kernel

Journal of Computational and Applied Mathematics
An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

The computation of wavelet coefficients of a function typically requires the computation of a large number of integrals. These integrals represent the inner product of that function with a wavelet function on different scales, or with the corresponding scaling function on a fine scale.We develop quadrature rules for those integrals that converge fast for piecewise smooth and singular functions. They do not require the evaluation of the scaling function, and the convergence does not depend on the smoothness of that function. The analysis and computation is based completely on the filter coefficients that define the scaling function. An application is presented from the field of electromagnetics, involving the inner product of a singular function with two-dimensional tensor-product wavelets.