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Subdivision schemes with nonnegative masks


Author: Xinlong Zhou
Journal: Math. Comp. 74 (2005), 819-839
MSC (2000): Primary 65D17, 26A15, 26A18, 39A10, 39B12
Published electronically: October 27, 2004
MathSciNet review: 2114650
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Abstract | References | Similar Articles | Additional Information

Abstract: The conjecture concerning the characterization of a convergent univariate subdivision algorithm with nonnegative finite mask is confirmed.


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  • 1. M. Bröker and X. Zhou, Characterization of continous, four-coefficient scaling functions via matrix spectral radius, SIAM J. Matrix Anal. Appl., 22 (2000), 242-257. MR 2001h:65169
  • 2. A. S. Cavaretta, W. Dahmen, and C. A. Micchelli, Stationary Subdivision, Mem. Amer. Math. Soc., 453 (1991). MR 92h:65017
  • 3. G. M. Chaikin, An algorithm for high speed curve generation, Comp. Graphics and Image. Proc., 3 (1974), 346-349.
  • 4. D. Colella and C. Heil, Characterizations of scaling functions: continuous solutions, SIAM J. Matrix Anal. Appl., 15 (1994), 496-518. MR 95f:26004
  • 5. I. Daubechies and J. C. Lagarias, Two-scale difference equations I. Existence and global regularity of solutions, SIAM J. Math. Anal., 22 (1991), 1388-1410. MR 92d:39001
  • 6. D. E. Gonsor, Subdivision algorithms with nonnegative masks generally converge, Adv. Comp. Math., 1 (1993), 215-221. MR 94e:65023
  • 7. R. -Q. Jia, Subdivision schemes in $L_p$ spaces, Advances in Comp. Math, 3 (1995), 309-341. MR 96d:65028
  • 8. R. -Q. Jia and D. -X. Zhou, Convergence of subdivision schemes associated with nonnegative masks, SIAM J. Matrix Anal. Appl., 21 (1999), 418-430.MR 2001a:42041
  • 9. A. A. Melkman, Subdivision schemes with non-negative masks always converge--unless they obviously cannot?, Ann. Numer. Math., 4 (1997), 451-460. MR 97i:41014
  • 10. C. A. Micchelli and H. Prautzsch, Uniform refinement of curves, Linear Algebra Appl., 114/115 (1989), 841-870. MR 90k:65088
  • 11. G. C. Rota and G. Strang, A note on the joint spectral radius, Indag. Math., 22 (1960), 379-381. MR 26:5434
  • 12. G. de Rham, Sur une courbe plane, J. Mathem. pures et appl., 39 (1956), 25-42. MR 19:842e
  • 13. J. N. Tsitsiklis and V. D. Blondel, The Lyapunov exponent and joint spectral radius of pairs of matrices are hard, when not impossible, to compute and to approximate, Mathematics of Control, Signals and Systems, 10 (1997), 31-41. MR 99h:65238a
  • 14. Y. Wang, Two-scale dilation equations and the cascade algorithm, Random and Computational Dynamics, 3 (1995), 289-309. MR 96m:42060
  • 15. Y. Wang, Subdivision schemes and refinement equations with nonnegative masks, J. Approx. Th., 113 (2001), 207-220. MR 2002i:42054
  • 16. D.-Z. Zhou, The p-norm joint spectral radius for even integers, Methods and Applications of Analysis, 5 (1) (1998), 39-54. MR 99e:42054

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Additional Information

Xinlong Zhou
Affiliation: Department of Mathematics, China Jiliang University, Hangzhou, China; Institute of Mathematics, University of Duisburg-Essen, D-47057 Duisburg, Germany
Email: zhou@math.uni-duisburg.de

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01712-0
Keywords: Cascade algorithm, joint spectral radius, nonnegative mask, subdivision scheme
Received by editor(s): December 13, 2002
Received by editor(s) in revised form: January 15, 2004
Published electronically: October 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society