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Title: Daubechies wavelets on intervals with application to BVPs (English)
Author: Finěk, Václav
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 49
Issue: 5
Year: 2004
Pages: 465-481
Summary lang: English
Category: math
Summary: In this paper, Daubechies wavelets on intervals are investigated. An analytic technique for evaluating various types of integrals containing the scaling functions is proposed; they are compared with classical techniques. Finally, these results are applied to two-point boundary value problems. (English)
Keyword: Daubechies wavelets
Keyword: computing scaling integrals
Keyword: two-point boundary value problems
MSC: 34B05
MSC: 42C40
MSC: 65N30
MSC: 65T60
idZBL: Zbl 1099.65146
idMR: MR2086089
DOI: 10.1023/B:APOM.0000048123.48173.c7
Date available: 2009-09-22T18:19:22Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] J. J. Benedetto, M. W.  Frazier: Wavelets: Mathematics and Applications. Studies in Advanced Mathematics.CRC Press, Boca Raton, 1994. MR 1247511
Reference: [2] A. Cohen: Wavelet Methods in Numerical Analysis. Handbook of Numerical Analysis, Vol. 7.P. G. Ciarlet at al. (eds.), North-Holland/Elsevier, Amsterdam, 2000, pp. 417–711. MR 1804747
Reference: [3] I.  Daubechies: Orthonormal bases of compactly supported wavelets.Commun. Pure Appl. Math. 41 (1988), 909–996. Zbl 0644.42026, MR 0951745, 10.1002/cpa.3160410705
Reference: [4] I. Daubechies: Ten Lectures on Wavelets.SIAM Publ., Philadelphia, 1992. Zbl 0776.42018, MR 1162107
Reference: [5] R. J. Duffin, A. C. Schaeffer: A class of nonharmonic Fourier series.Trans. Amer. Math. Soc. 72 (1952), 341–366. MR 0047179, 10.1090/S0002-9947-1952-0047179-6
Reference: [6] V.  Finěk: Daubechies wavelets and two-point boundary value problems.Preprint, TU Dresden, 2001.
Reference: [7] R.  Glowinski, W.  Lawton, M.  Ravachol, and E. Tenenbaum: Wavelet solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension.Computing Methods in Applied Sciences and Engineering, Proc. 9th Int. Conf. Paris, 1990, pp. 55–120. MR 1102021
Reference: [8] Ch. Grossmann, H.-G.  Roos: Numerik partieller Differentialgleichungen, 2. edition.Teubner, Stuttgart, 1994. MR 1312608
Reference: [9] C. Heil: Wavelets and frames, Signal processing, Part  I: Signal processing theory.Proc. Lect, , Minneapolis, 1988.
Reference: [10] A. Kunoth: Wavelet Methods—Elliptic Boundary Value Problems and Control Problems. Advances in Numerical Mathematics.Teubner, Stuttgart, 2001. MR 1852351
Reference: [11] W. Lawton: Necessary and sufficient conditions for constructing orthonormal wavelet bases.J.  Math. Phys. 32 (1991). Zbl 0757.46012, MR 1083085
Reference: [12] A. K. Louis, P.  Maas, A. Rieder: Wavelets: Theorie und Anwendungen.Teubner, Stuttgart, 1994. (German) MR 1371382
Reference: [13] Y.  Meyer: Ondelettes et Opérateurs  I—Ondelettes.Hermann Press, Paris, 1990, English translation: Wavelets and Operators, Cambridge University Press, (1992). Zbl 0694.41037, MR 1085487
Reference: [14] Y. Meyer: Ondelettes sur l’intervalle.Rev. Math. Iberoamer. 7 (1991), 115–133. (French) Zbl 0753.42015, MR 1133374
Reference: [15] Z.-Ch.  Shann, J.-Ch.  Yan: Quadratures involving polynomials and Daubechies’ wavelets.Preprint, National Central University, Chung-Li, Taiwan, R.O.C., April, (1994).
Reference: [16] W.-Ch. Shann, J.-Ch. Xu: Galerkin-wavelet methods for two-point boundary value problems.Numer. Math. 63 (1992), 123–144. Zbl 0771.65050, MR 1182515, 10.1007/BF01385851
Reference: [17] W.  Sweldens, R.  Piessens: Quadrature formulae and asymptotic error expansions for wavelet approximation of smooth functions.SIAM J.  Numer. Anal. 31 (1994), 1240–1264. MR 1286226, 10.1137/0731065
Reference: [18] P. Wojtaszczyk: A Mathematical Introduction to Wavelets.Cambridge University Press, Cambridge, 1997. Zbl 0865.42026, MR 1436437


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