How high is high-dimensional?

  • Ian H. Sloan

    University of New South Wales, Sydney, Nsw, Australia
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Consider the problem of evaluating the d-dimensional integral

Id(f) := ∫10 · · · ∫10 f(x1,…, xd) dx1 … dxd = ∫[0,1]d f(x) dx,

where f is a continuous function over the d-dimensional unit cube.

To take up immediately the question in the title, let us ask: how large can we reasonably take d to be?