Subdivision schemes with nonnegative masks
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Abstract:
The conjecture concerning the characterization of a convergent univariate subdivision algorithm with nonnegative finite mask is confirmed.References
- Markus Bröker and Xinlong Zhou, Characterization of continuous, four-coefficient scaling functions via matrix spectral radius, SIAM J. Matrix Anal. Appl. 22 (2000), no. 1, 242–257. MR 1779727, DOI 10.1137/S0895479897323750
- Alfred S. Cavaretta, Wolfgang Dahmen, and Charles A. Micchelli, Stationary subdivision, Mem. Amer. Math. Soc. 93 (1991), no. 453, vi+186. MR 1079033, DOI 10.1090/memo/0453
- G. M. Chaikin, An algorithm for high speed curve generation, Comp. Graphics and Image. Proc., 3 (1974), 346-349.
- David Colella and Christopher Heil, Characterizations of scaling functions: continuous solutions, SIAM J. Matrix Anal. Appl. 15 (1994), no. 2, 496–518. MR 1266600, DOI 10.1137/S0895479892225336
- Ingrid Daubechies and Jeffrey C. Lagarias, Two-scale difference equations. I. Existence and global regularity of solutions, SIAM J. Math. Anal. 22 (1991), no. 5, 1388–1410. MR 1112515, DOI 10.1137/0522089
- Daniel E. Gonsor, Subdivision algorithms with nonnegative masks generally converge, Adv. Comput. Math. 1 (1993), no. 2, 215–221. MR 1230258, DOI 10.1007/BF02071386
- Rong Qing Jia, Subdivision schemes in $L_p$ spaces, Adv. Comput. Math. 3 (1995), no. 4, 309–341. MR 1339166, DOI 10.1007/BF03028366
- Rong-Qing Jia and Ding-Xuan Zhou, Convergence of subdivision schemes associated with nonnegative masks, SIAM J. Matrix Anal. Appl. 21 (1999), no. 2, 418–430. MR 1718338, DOI 10.1137/S0895479898342432
- Avraham A. Melkman, Subdivision schemes with non-negative masks converge always—unless they obviously cannot?, Ann. Numer. Math. 4 (1997), no. 1-4, 451–460. The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin. MR 1422696
- Charles A. Micchelli and Hartmut Prautzsch, Uniform refinement of curves, Linear Algebra Appl. 114/115 (1989), 841–870. MR 986909, DOI 10.1016/0024-3795(89)90495-3
- Gian-Carlo Rota and Gilbert Strang, A note on the joint spectral radius, Nederl. Akad. Wetensch. Proc. Ser. A 63 = Indag. Math. 22 (1960), 379–381. MR 0147922, DOI 10.1016/S1385-7258(60)50046-1
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- John N. Tsitsiklis and Vincent D. Blondel, The Lyapunov exponent and joint spectral radius of pairs of matrices are hard—when not impossible—to compute and to approximate, Math. Control Signals Systems 10 (1997), no. 1, 31–40. MR 1462278, DOI 10.1007/BF01219774
- Yang Wang, Two-scale dilation equations and the cascade algorithm, Random Comput. Dynam. 3 (1995), no. 4, 289–307. MR 1362775
- Yang Wang, Subdivision schemes and refinement equations with nonnegative masks, J. Approx. Theory 113 (2001), no. 2, 207–220. MR 1876323, DOI 10.1006/jath.2001.3623
- Ding-Xuan Zhou, The $p$-norm joint spectral radius for even integers, Methods Appl. Anal. 5 (1998), no. 1, 39–54. MR 1631335, DOI 10.4310/MAA.1998.v5.n1.a2
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
- Received by editor(s): December 13, 2002
- Received by editor(s) in revised form: January 15, 2004
- Published electronically: October 27, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 819-839
- MSC (2000): Primary 65D17, 26A15, 26A18, 39A10, 39B12
- DOI: https://doi.org/10.1090/S0025-5718-04-01712-0
- MathSciNet review: 2114650