Article Accepted Version Chernov, A. (2012) Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex. It is advisable to refer to the publisher's version ifâ€¦ (More)

We extend the general framework of the Multilevel Monte Carlo method to multilevel estimation of arbitrary order central statistical moments. In particular, we prove that under certain assumptions,â€¦ (More)

It is advisable to refer to the publisher's version if you intend to cite from the work. Abstract. Galerkin discretizations of integral operators in R d require the evaluation of integrals S (1) Sâ€¦ (More)

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a newâ€¦ (More)

We develop a complete convergence theory for the Maximum Entropy method based on moment matching for a sequence of approximate statistical moments estimated by the Multilevel Monte Carlo method.â€¦ (More)

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d â‰¥ 2. Optimal error estimates are established in the case of Sobolevâ€¦ (More)

We introduce and analyze a family of algorithms for an efficient numerical approximation of integrals of the form I = âˆ« C(1) âˆ« C(2) F (x, y, yâˆ’x)dydx where C, C are d-dimensional parallelotopes (i.e.â€¦ (More)