Tractability of multivariate approximation over a weighted unanchored Sobolev space: Smoothness sometimes hurts

Arthur G. Werschulz & Henryk Wozniakowski
We study d-variate approximation for a weighted unanchored Sobolev space having smoothness m ≥ 1. Folk wisdom would lead us to believe that this problem should become easier as its smoothness increases. This is true if we are only concerned with asymptotic analysis: the nth minimal error is of order n^-(m-δ) for any δ > 0. However, it is unclear how long we need to wait before this asymptotic behavior kicks in. How does this...
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