Adaptive sampling recovery B-spline Besov space Quasi-interpolant wavelet representation
Issue Date:
2011
Publisher:
Advances in Computational Mathematics
Citation:
Volume: 34 Issue: 1 Page : 1-41
Abstract:
We propose an approach to study optimal methods of adaptive sampling recovery of functions by
sets of a finite capacity which is measured by their cardinality or pseudo-dimension. Let W ?? Lq, 0 < q ??
??, be a class of functions on Id. For B a subset in Lq, we define a sampling recovery method with the free
choice of sample points and recovering functions from B as follows. For each f ?? W we choose n sample
points. This choice defines n sampled values. Based on these sampled values, we choose a function from B
for recovering f. The choice of n sample points and a recovering function from B for each f ?? W defines a
sampling recovery method SB
n by functions in B.
