Title: Asymptotic error expansion of wavelet approximations of smooth functions .2
Authors: Sweldens, Wim ×
Piessens, Robert #
Issue Date: Sep-1994
Publisher: Springer
Series Title: Numerische Mathematik vol:68 issue:3 pages:377-401
Abstract: We generalize earlier results concerning an asymptotic error expansion of wavelet approximations. The properties of the monowavelets, which are the building blocks for the error expansion, are studied in more detail, and connections between spline wavelets and Euler and Bernoulli polynomials are pointed out. The expansion is used to compare the error for different wavelet families. We prove that the leading terms of the expansion only depend on the multiresolution subspaces V(j) and not on how the complementary subspaces W(j) are chosen. Consequently, for a fixed set of subspaces V(j), the leading terms do not depend on the fact whether the wavelets are orthogonal or not. We also show that Daubechies' orthogonal wavelets need, in general, one level more than spline wavelets to obtain an approximation with a prescribed accuracy. These results are illustrated with numerical examples.
ISSN: 0029-599X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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