Locally Supported, Piecewise Polynomial Biorthogonal Wavelets on Nonuniform Meshes

Constructive Approximation

Volumn 19, Issue 4, 2003, Pages 477-508

  Stevenson, Rob ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Locally supported biorthogonal wavelets; Nonuniform meshes; Riesz bases

Indexed keywords

EID: 0242360743     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-003-0545-2     Document Type: Article

References (17)

1. C. CANUTO, A. TABACCO, K. URBAN (1999): The wavelet element method, Part I: Construction and analysis. Appl. Comput. Harmonic Anal., 6:1-52.
2. J. M. CARNICER, W. DAHMEN, J. M. PEÑA (1996): Local decomposition of refinable spaces and wavelets. Appl. Comput. Harmonic Anal., 3:127-153.
3. A. COHEN (2000): Wavelet methods in numerical analysis. In: Handbook of Numerical Analysis, Vol. VII (P. G. Ciarlet, J. L. Lions, eds.). Amsterdam: North-Holland, pp. 417-711.
4. A. COHEN, I. DAUBECHIES, J. C. FEAUVEAU (1992): Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 45:485-560.
5. A. COHEN, L. M. ECHEVERRY, Q. SUN (2000): Finite element wavelets. Technical report, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie. Submitted.
6. W. DAHMEN (1991): Some remarks on multiscale transformations, stability and biorthogonality. In: Curves and Surfaces II (P. J. Laurent, A. Le Méhauté, L. L. Schumaker, eds.). Boston: A. K. Peters, pp. 1-32.
7. W. DAHMEN (1996): Stability of multiscale transformations. J. Fourier Anal. Appl., 4:341-362.
8. W. DAHMEN (1997): Wavelet and multiscale methods for operator equations. Acta Numerica, 6:55-228.
9. W. DAHMEN, R. SCHNEIDER (1999): Composite wavelet bases for operator equations. Math. Comp., 68:1533-1567.
10. W. DAHMEN, R. SCHNEIDER (1999): Wavelets on manifolds I: Construction and domain decomposition. SIAM J. Math. Anal., 31:184-230.
11. W. DAHMEN, R. P. STEVENSON (1999): Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal., 37(1):319-352.
12. I. DAUBECHIES, I. GUSKOV, P. SCHRÖDER, W. SWELDENS (1999): Wavelets on irregular point sets. Philos. Trans. Roy. Soc. London A, 357(1760):2397-2413.
13. G.C. DONOVAN, J. GERONIMO, D. P. HARDIN (1999): Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. SIAM J. Math. Anal., 30(5):1029-1056.
14. G. C. DONOVAN, J. GERONIMO, D. P. HARDIN (2000): Compactly supported, piecewise affine scaling functions on triangulations. Constr. Approx., 16(2):201-219.
15. T. N. T. GOODMAN (2000): Biorthogonal refinable spline functions. In: Curve and Surface Fitting: Saint-Malo 1999 (A. Cohen, C. Rabut, L. L. Schumaker, eds.). Nashville, TN: Vanderbilt University Press, pp. 1-8.
16. P. OSWALD (1994): Multilevel Finite Element Approximation: Theory and Applications. Stuttgart: B. G. Teubner.
17. W. SWELDENS (1998): The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal., 29(2):511-546.