Interpolatory subdivision schemes and wavelets

Journal of Approximation Theory

Volumn 86, Issue 1, 1996, Pages 41-71

  Micchelli, Charles A ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030187586     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0054     Document Type: Article

References (21)

1. 1. R. ANSARI, G. GUILLEMOT, AND J. F. KAISER, Wavelet Construction Using Lagrange halfband filters, IEEE Trans. Circuits Syst. 38 (1991), 1116-1118.
2. 2. A. S. CAVARETTA, W. DAHMEN, AND C. A. MICCHELLI, Stationary Subdivision Schemes, Mem. Amer. Math. Soc. 93, 1-186.
3. 3. I. DAUBECHIES, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
4. 4. I. DAUBECHIES, Ten Lectures on Wavelets, in "CBMS-NSF Regional Conference in Applied Mathematics #61," SIAM, Philadelphia, 1992.
5. 5. G. DESLAURIERS, J. DUBOIS, AND S. DUBUC, Multidimensional iterative interpolation, Canad. J. Math. 43 (1991), 297-312.
6. 6. G. DESLAURIERS AND S. DUBUC, Symmetric iterative interpolation processes, Constr. Approx. 5 (1989), 49-68.
7. 7. G. DESLAURIERS AND S. DUBUC, Continuous iterative interpolation processes, preprint.
8. 8. S. DUBUC, Interpolation through an iterative scheme, J. Math. Anal. Appl. 114 (1986), 185-204.
9. 9. S. DUBUC AND F. NEKKA, One dimensional fractal functions, measures and distributions, in "Fractals in the Fundamental and Applied Sciences" (H.-O. Peitzer, J. M. Henriques, and L. F. Penedo, Eds.), pp. 111-121, Elsevier, Amsterdam/New York 1991.
10. 10. S. DUBUC AND F. NEKKA, General interpolation schemes for the generation of irregular surfaces, Constr. Approx. 9 (1999), 525-542.
11. 11. N. DYN, Subdivision schemes in computer-aided geometric design, in "Advances in Numerical Analysis, Vol. II, Wavelets, Subdivision Algorithms and Radial Basis Functions" (W. Light, Ed.), pp. 36-104, Clarendon, Oxford, 1992.
12. 12. N. DYN AND D. LEVIN, Interpolating subdivision schemes for the generation of curves and surfaces, ISNM94, Birkhäuser, Basel, 1990.
13. 13. T. N. T. GOODMAN AND C. MICCHELLI, Orthonormal cardinal functions, in "Wavelets-Theory, Algorithms and Applications" (C. K. Chui, L. Montefusco, and L. Puccio, Eds.), pp. 53-88, Academic Press, San Diego, 1994.
14. 14. R. Q. JIA AND C. A. MICCHELLI, Using the refinement equation for the construction of pre-wavelets. II. Power of two, in "Curves and Surfaces" (P. J. Laurent, A. Le Méhauté, and L. L. Schumaker, Eds.), pp. 209-246, Academic Press, San Diego, 1991.
15. 15. Y. MEYER, Wavelets with compact support, in "Zygmund Lectures," University of Chicago, May 1987 (private communication given in Ref. [3] above).
16. 16. C. A. MICCHELLI AND H. PRAUTZSCH, Refinement and subdivision for spaces of integer translates of a compactly supported function, in "Numerical Analysis" (D. F. Griffith and G. A. Watson, Eds.), pp. 192-222, Academic Press, New York, 1987.
17. 17. J. P. MONGEAU, G. DESLAURIERS, AND S. DUBUC, Continuous and differentiable multidimensional iterative interpolation, LAA 180 (1993), 95-120.
18. 18. J. P. MONGEAU, S. DUBUC, AND G. DESLAURIERS, Iterative interpolation process and its application to a data compression process, preprint.
19. 19. R. Qu, An interpolatory subdivision algorithm for surfaces over arbitrary triangulations, preprint.
20. 20. G. STRANG, The optimal coefficients in Daubechies wavelets, Physica D 60 (1992), 239-244.
21. 21. R. J. WALKER, "Algebraic Curves," Princeton Univ. Press, Princeton, NJ, 1950.