Smoothness analysis of subdivision schemes on regular grids by proximity

SIAM Journal on Numerical Analysis

Volumn 46, Issue 4, 2008, Pages 2169-2182

  Grohs, Philipp ^a  

^a INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE   (Austria)

Author keywords

Lazy wavelets; Linear subdivision schemes; Multivariate subdivision; Nonlinear subdivision schemes; Smoothness

Indexed keywords

POLYNOMIAL APPROXIMATION; VECTORS;

LAZY WAVELETS; LINEAR SUBDIVISION SCHEMES; MULTIVARIATE SUBDIVISION; NONLINEAR SUBDIVISION SCHEMES; SMOOTHNESS;

NONLINEAR ANALYSIS;

EID: 55349135938     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/060669759     Document Type: Article

References (17)

1. A. S. CAVARETTA, C. A. MICCHELLI, AND W. DAHMEN, Stationary Subdivision, American Mathematical Society, Boston, MA, 1991.
2. D. L. DONOHO AND T. P. YU, Deslauriers-Dubuc: Ten years after, in Spline Functions and the Theory of Wavelets, S. Dubuc and G. Deslauriers, eds., CRM Proc. Lecture Notes 18, American Mathematical Society, Providence, HI, 1999, pp. 355-370.
3. D. L. DONOHO, Interpolating Wavelet Transforms, Technical report, Stanford University, Stanford, CA, 1992; also available from http://www-stat.stanford.edu/~donoho/Reports/1992/interpol.pdf.
4. D. L. DONOHO, Wavelet-type representation of Lie-valued data, in Proceedings of the IMI Approximation and Computation Meeting, Charleston, SC, Industrial Mathematics Institute, Columbia, SC, 2001.
5. N. DYN, D. LEVIN, AND J. A. GREGORY, A 4,-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Design, 4 (1987), pp. 257-268.
6. N. DYN, Subdivision schemes in CAGD, in Advances in Numerical Analysis Vol. II, W. A. Light, ed., Oxford University Press, London, 1992, pp. 36-104.
7. P. GROHS, Smoothness Analysis of Nonlinear Subdivision Schemes on Regular Grids, Ph.D. thesis, Vienna University of Technology, Wien, Austria, 2007.
8. L. KOBBELT, Interpolatory subdivision on open quadrilateral nets with arbitrary topology, Comput. Graph. Forum, 15 (1996), pp. 409-420.
9. J. NASH, The imbedding problem for Riemannian manifolds, Ann. of Math., 63 (1956), pp. 20-63.
10. I. U. RAHMAN, I. DRORI, V. C. STODDEN, D. L. DONOHO, AND P. SCHRÖDER, Multiscale representations for manifold-valued data, Multiscale Model. Simul., 4 (2005), pp. 1201-1232.
11. M. SPIVAK, A Comprehensive Introduction to Differential Geometry, Vol. I-V, Publish or Perish, Boston, MA, 1979.
12. 1 analysis of subdivision schemes on manifolds by proximity, Comput. Aided Geom. Design, 22 (2005), pp. 593-622.
13. J. WALLNER, E. NAVA YAZDANI, AND P. GROHS, Smoothness properties of Lie group subdivision schemes, Multiscale Model. Simul., 6 (2007), pp. 493-505.
14. J. WALLNER, Smoothness analysis of subdivision schemes by proximity, Constr. Approx., 24 (2006), pp. 289-318.
15. G. XIE AND T. P.-Y. YU, Smoothness equivalence properties of manifold-valued data subdivision schemes based on the projection approach, SIAM J. Numer. Anal., 45 (2007), pp. 1220-1225.
16. T. P.-Y. YU, Cutting corners on the sphere, in Wavelets and Splines: Athens 2005, G. Chen and M.-J. Lai, eds., Nashboro Press, Brentwood, TN, 2006, pp. 496-506.
17. D. X. ZHOU, Stability of refinable functions, multiresolution analysis, and haar bases, SIAM J. Math. Anal., 27 (1996), pp. 891-904.