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

Journal of Computational and Applied Mathematics

Volumn 180, Issue 1, 2005, Pages 119-135

  Huybrechs, Daan ^a   Vandewalle, Stefan ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Numerical integration; Quadrature; Singular functions; Wavelets

Indexed keywords

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; INTEGRAL EQUATIONS; INTEGRATION;

PIECEWISE INTEGRATION; QUADRATURE RULE; SINGULAR FUNCTIONS;

WAVELET TRANSFORMS;

EID: 17644368564     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.10.005     Document Type: Article

References (13)

1. M. Abramowitz I.A. Stegun Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1965 Dover Publications New York
2. A. Barinka T. Barsch S. Dahlke M. Konik Some remarks on quadrature formulas for refinable functions and wavelets Z. Angew. Math. Mech. 81 12 2001 839-855.
3. G. Beylkin R.R. Coifman V. Rokhlin Fast wavelet transforms and numerical algorithms I Comm. Pure Appl. Math. 44 1991 141-183
4. R. Burden J. Faires Numerical Analysis fourth ed. 1989 PWS-Kent Publishing Company Boston
5. A. Cohen I. Daubechies J.-C. Feauveau Biorthogonal bases of compactly supported wavelets Comm. Pure Appl. Math. 55 1992 485-560
6. D. Colton R. Kress Integral Equation Methods in Scattering Theory 1983 Wiley New York
7. W. Dahmen C.A. Micchelli Using the refinement equation for evaluating integrals of wavelets SIAM J. Numer. Anal. 30 2 1993 507-537
8. I. Daubechies Orthonormal bases of compactly supported wavelets Comm. Pure Appl. Math. 41 1988 909-996
9. P.J. Davis P. Rabinowitz Methods of Numerical Integration 1984 Academic Press Inc. New York
10. W. Gautschi, L. Gori, F. Pitolli, Gauss quadrature for refinable weight functions, Appl. Comput. Harmon. Anal. (8) (2000) 249-257.
11. W. Hackbusch, Integral Equations: Theory and Numerical Treatment, vol. 120, International Series of Numerical Mathematics, Birkhäuser Verlag, Basel, Switzerland, 1995.
12. D. Huybrechs J. Simoens S. Vandewalle A note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel J. Comput. Appl. Math. 172 2 2004 233-246
13. W. Sweldens R. Piessens Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions SIAM J. Numer. Anal. 31 4 1994 1240-1264