Abstract
We study bounds on the exponents of sparse grids for L 2‐discrepancy and average case d‐dimensional integration with respect to the Wiener sheet measure. Our main result is that the minimal exponent of sparse grids for these problems is bounded from below by 2.1933. This shows that sparse grids provide a rather poor exponent since, due to Wasilkowski and Woźniakowski [16], the minimal exponent of L 2‐discrepancy of arbitrary point sets is at most 1.4778. The proof of the latter, however, is non‐constructive. The best known constructive upper bound is still obtained by a particular sparse grid and equal to 2.4526....
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Plaskota, L. The exponent of discrepancy of sparse grids is at least 2.1933. Advances in Computational Mathematics 12, 3–24 (2000). https://doi.org/10.1023/A:1018900715321
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DOI: https://doi.org/10.1023/A:1018900715321