Kai Bittner
Periodic Spline Wavelets on Sparse Grids
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

41A15 Spline approximation

41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)

Abstract: We consider Boolean sums of univariate interpolation operators which
derine multivariante j-th order blending interpolation operators on
sparse grids. Sample spaces are defined as range of the blending
operators. Sample and wavelet spaes have significantly lower dimension
and good approximation order for certain function spaces. Fast
decomposition and reconstruction algorithms for bivariate spline
wavelets, based on algorithms for univariate functions, are
described. Operation vounts for the algorithms are given and it is
shown, that the complexity depends linearly on the dimension of
sample spaces.
Keywords: wavelets, splines, multivariante periodic interpolation, Boolean sums, sparse grids