Multivariate problems occur in many applications. These problems are defined on spaces of d-variate functions and d can be huge – in the hundreds or even in the thousands. Some high-dimensional… Expand

We study bounds on the classical ∗-discrepancy and on its inverse. Let n∞(d, e) be the inverse of the ∗-discrepancy, i.e., the minimal number of points in dimension d with the ∗-discrepancy at most… Expand

This paper addresses the problem of computing an approximation to the largest eigenvalue of an $n \times n$ large symmetric positive definite matrix with relative error at most $\varepsilon $.Expand

Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems.Expand

We study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical Wiener sheet measure. To derive the average case… Expand