We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomialâ€¦ (More)

There has been an increasing interest in studying high dimensional numerical integration. This problem occurs in many applications. In particle physics and in finance the number of variables can beâ€¦ (More)

It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of theâ€¦ (More)

We study bounds on the classical âˆ—-discrepancy and on its inverse. Let nâˆž(d, Îµ) be the inverse of the âˆ—-discrepancy, i.e., the minimal number of points in dimension d with the âˆ—-discrepancy at mostâ€¦ (More)

We give a path integral prescription for the pair correlation function of Wilson loop observables on the worldvolume of a Dbrane in the bosonic string theory in flat spacetime. We determine theâ€¦ (More)

We prove that Lâˆž-approximation of C âˆž-functions defined on [0, 1]d is intractable and suffers from the curse of dimensionality. This is done by showing that the minimal number of linear functionalsâ€¦ (More)

We study Monte Carlo methods (randomized algorithms) that use only a small number of random bits instead of more general random numbers for the computation of sums and integrals. To approximate N ?1â€¦ (More)

We prove the curse of dimensionality for multivariate integration of Ck functions. The proofs are based on volume estimates for k = 1 together with smoothing by convolution. This allows us to obtainâ€¦ (More)