Please use this identifier to cite or link to this item:
https://doi.org/10.1007/s002110100265
Title: | Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets |
Authors: | Jia, R.-Q. Jiang, Q. Lee, S.L. |
Issue Date: | May-2002 |
Citation: | Jia, R.-Q., Jiang, Q., Lee, S.L. (2002-05). Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets. Numerische Mathematik 91 (3) : 453-473. ScholarBank@NUS Repository. https://doi.org/10.1007/s002110100265 |
Abstract: | The cascade algorithm with mask a and dilation M generates a sequence φn, n = 1, 2,..., by the iterative process φn(x) = ∑αεℤs a(α)φn-1(Mx - α) x ε ℝs, from a starting function φ0, where M is a dilation matrix. A complete characterization is given for the strong convergence of cascade algorithms in Sobolev spaces for the case in which M is isotropic. The results on the convergence of cascade algorithms are used to deduce simple conditions for the computation of integrals of products of derivatives of refinable functions and wavelets. |
Source Title: | Numerische Mathematik |
URI: | http://scholarbank.nus.edu.sg/handle/10635/103071 |
ISSN: | 0029599X |
DOI: | 10.1007/s002110100265 |
Appears in Collections: | Staff Publications |
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