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Abstract:
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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. |