THE RELATION BETWEEN nTH MINIMAL ERRORS OF TWO CLASSES OF INFORMATION FOR APPROXIMATION IN H（O..）LDER SPACE

摘要

Let H = Cr'α([0, 1]d) be Holder space and G = L2([0, 1]d) with the inner product given byThis paper considers the embedding operator S: H → G, S(f) = f, f ∈ H. We prove thatwhere en(S, std) and en(S,Aall) denote the nth minimal error of standard and linear information respectively in the worst case, average case and randomized settings, and C is a constant.