Group Seminar: QMC: Randomized algorithms for L2-approximation

Speaker: David Krieg (Friedrich-Schiller-Universität Jena), Location: SP2 416-1

QMC: Randomized algorithms for L2-approximation

Speaker: David Krieg (Friedrich-Schiller-Universität Jena)
Date: January 17, 2018 12:00
Location: SP2 416-1

We discuss a randomized algorithm for the approximation in an arbitrary L2-space that requests at most n function values of the target function. The target function is assumed to lie in the unit ball of a Hilbert space which is compactly embedded in L2. In many examples, this algorithm is optimal up to a multiplicative constant which does neither depend on n nor on the dimension of the underlying domain. It is even optimal among all algorithms that ask for n pieces of arbitrary linear information. The talk is based on [1]. [1] K.: Optimal Monte Carlo methods for L2-approximation. ArXiv e-prints, 2017. arXiv:1705.04567 [math.NA]