Convergence of nonstationary cascade algorithms

Numerische Mathematik

Volumn 84, Issue 1, 1999, Pages 1-33

  Goodman, T N T ^a   Lee, S L ^b  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844454463     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050462     Document Type: Article

References (42)

1. deBoor, C., DeVore R., Ron A. (1993): On the construction of multivariate (pre)wavelets. Constr. Approx. 9, 123-166
2. Buhmann, M.D., Micchelli, C.A (1994): Using two-slanted matrices for subdivision. Proc. London Math. Soc. 69, 428-448
3. Cavaretta, A.S., Dahmen W., Micchelli, C.A. (1991): Stationary subdivision. Memoir Amer. Math. Soc. 93, 1-186
4. Chui, K. Charles, Lian, J.A. (1996): A study of orthonormal multi-wavelets. Applied Numerical Mathematics 20, 273-298
5. Cohen, A., Daubechies, I. (1992): A stability criterion for biorthogonal wavelet bases and their related subband coding scheme. Duke Math. J. 68, 313-335
6. Cohen, A., Daubechies, I., Plonka G. (1997): Regularity of refinable functions. J. Fourier Anal. and Appl. 3, 295-323
7. Cohen, A., Gröchenig K., Villemoes L. (1996): Regularity of multivariate refinable functions. Preprint
8. Daubechies, I. (1988): Orthonormal bases of compactly supported wavelets. Comm. Pure and Appl. Math. 41, 909-996
9. Daubechies, I., Lagaria, J.C. (1991): Two-scale difference equations I. Existence and global regularity of solutions. SIAM J. Math. Anal. 22, 1388-1410
10. Daubechies, I., Lagaria, J.C. (1992): Two-scale difference equations II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23, 1031-1079
11. Derfel, G., Dyn, N., Levin, D. (1995): Generalized functional equations and subdivision schemes. J. Approx. Theory 30, 272-297
12. Dyn, N., Levin D., Micchelli, C.A. (1990): Using parameters to increase smoothness of curves and surfaces generated by subdivision. CAGD 7, 91-106
13. Dyn, N., Levin, D. (1992): Stationary and nonstationary subdivision schemes. In: Mathmetaical Methods on Computer Aided Geometric Design II. (Lyche, T., Schumaker, L.L. eds.), Birkhauser, Basel, pp. 209-216
14. Dyn, N., Levin, D. (1995): Analysis of asymptotically equivalent binary subdivision schemes. J. Math. Anal, and Applic. 193, 594-621
15. Eirola, T. (1992): Sobolev characterization of solutions of dilation equations. SIAM J. Math. Anal. 23, 1015-1030
16. Goh, S.S., Lee, S.L., Teo, K.M. (1999): Multidimensional periodic multiwavelets. J. Approx. Theory 98, 72-103
17. Goodman, T.N.T., Micchelli, C.A., Ward, J. (1995): Spectral radius formulas for subdivision operators. In: Recent Advances in Wavelet Analysis. Schumaker, L.L., Webb, G. (eds), Academic Press, 335-360
18. Bin Han, Jia, R.Q.: Multivariate refinement equations and convergence of subdivision schemes, to appear in SIAM J. Math. Anal.
19. Heil, C., Colella, D. (1996): Matrix refinement equations: Existence and Uniqueness. J. Fourier Anal, and Appl. 2, 363-377
20. Heil, C., Strang, G., Stella, V. (1996): Approximation by translates of refinable functions. Numer. Math. 73, 75-94
21. Hervé, L. (1995): Construction et regularite des fonctions d' echelle. SIAM J. Math. Anal. #5, 26, 1361-1385
22. p spaces. Advances in Computational Mathematics 3, 309-341
23. Jia, R.Q., Zuowei Shen (1994): Multiresolution and wavelets, Proc. Ldinburgh Math. Soc. 37, 271-300
24. Jia, R.Q.: Characterization of smoothness of multivariate refinable functions in Sobolev spaces, to appear in Trans. Amer. Math. Soc.
25. Jia, R.Q. (1996): Approximation properties of multivariable wavelets. Preprint, University of Alberta
26. Jia, R.Q., Riemenschneider, S., Zhou, D.X. (1996): Smoothness of multiple refinable functions and multiple wavelets. Preprint, University of Alberta
27. Jia, R.Q., Zhang, S.: Spectral properties of the transition operator associated to a multivariate refinement equation. Preprint, University of Alberta, Canada
28. Jiang, Q., Shen Zuowei (1996): On the existence and weak stability of matrix refinable functions. Preprint, National University of Singapore, to appear in Constr. Approx.
29. Jiang, Q. (1996): Multivariate matrix refinable functions with arbitrary matrix dilation. Preprint, National University of Singapore, to appear in Trans. Amer. Math. Soc.
30. Jiang, Q. (1998): On the regularity of matrix refinable functions, SIAM J. Math. Anal. 29, 1157-1176
31. Lawton, W., (1991): Necessary and sufficient conditions for constructing orthonormal wavelets, J. Math. Phys. 32, 52-61
32. Lawton, W., (1991): Multilevel properties of the wavelet-Galerkin operator. J. Math. Phys. 32, 1440-1443
33. Lawton, W., Lee, S.L., Zuowei Shen (1997): Stability and orthonormality of multidimensional refinable functions. SIAM J. Math. Analysis 28, 999-1014
34. Lawton, W., Lee, S.L., Zuowei Shen (1998): Convergence of multidimensional cascade algorithm. Numer. Math. 78, 427-438
35. Li Qi (1998): Nonstationary multiresolution analysis and nonstationary orthonormal wavelets. M.Sc. Thesis, National University of Singapore
36. d. Appl. Comp. Harmonic Anal. 2, 230-242
37. Micchelli, C.A., Thomas Sauer (1996): Regularity of multiwavelets. Preprint, Watson Research Center, IBM
38. Plonka, G., (1997): Approximation order provided by refinable function vectors. Constr. Approx. 13, 221-244
39. Shen, Z., (1998): Refinable function vector. SIAM J. Math. Anal. 29, 235-250
40. Strang, G. (1996): Eigenvalues of (↓, 2) H and convergence of cascade algorithm. IEEE Trans. SP 44
41. Villemoes, L. (1992): Energy moments in time and frequency for two-scale difference equation solutions and wavelets. SIAM J. Math. Anal. 23, 1519-1543
42. Villemoes, L. (1994): Wavelet analysis of refinable equations. SIAM J. Math. Anal. 25, 1433-1460