Recently quasi-Monte Carlo algorithms have been successfully used for multivariate integration of high dimension d, and were signiicantly more eecient than Monte Carlo algorithms. The existing theoryâ€¦ (More)

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 toâ€¦ (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 study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spacesâ€¦ (More)

We study multivariate tensor product problems in the worst case and average case settings. They are deened on functions of d variables. For arbitrary d, we provide explicit upper bounds on the costsâ€¦ (More)

We study multivariate integration in the worst case setting and multivariate approximation in the average case setting for various classes of functions of d variables with arbitrary d. We considerâ€¦ (More)

Interestingly, a general theory of optimal algorithms that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is providedâ€¦ (More)

We study the "-approximation of linear multivariate problems deened over weighted tensor product Hilbert spaces of functions f of d variables. A class of weighted tensor product (WTP) algorithms isâ€¦ (More)