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|Title:||Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets|
|Source:||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|
|Appears in Collections:||Staff Publications|
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