Subdivision schemes with nonnegative masks

Zhou, Xinlong

doi:10.1090/S0025-5718-04-01712-0

Subdivision schemes with nonnegative masks
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Math. Comp. 74 (2005), 819-839 Request permission

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