L. Plaskota and G.W. Wasilkowski

The exact exponent of sparse grid quadratures in the weighted case

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Abstract.   This paper provides a lowe bound on the exponent of tractability for sparse grid quadratures for multivariate integration of functions from a certain class of weighted tensor product spaces. This lower bound is sharp since it matches a corresponding upper bound of Wasilkowski and Wozniakowski (1999). It also shows that, for slowly decresing weights, the exponent of sparse grid quadratures is far from being optimal.

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