3 papers
math.NA2021
Recovery of Sobolev functions restricted to iid sampling
David Krieg, Erich Novak, Mathias Sonnleitner
We study -approximation and integration for functions from the Sobolev space and compare optimal randomized (Monte Carlo) algorithms with algorithms that can only u…
math.NA2020
Lower Bounds for the Error of Quadrature Formulas for Hilbert Spaces
Aicke Hinrichs, David Krieg, Erich Novak +1
We prove lower bounds for the worst case error of quadrature formulas that use given sample points $\X_n = \{ x_1, \dots , x_n \}$. We are mainly interested in optimal point sets $…
math.PR2019
Expected dispersion of uniformly distributed points
Aicke Hinrichs, David Krieg, Robert J. Kunsch +1
The dispersion of a point set in is the volume of the largest axis parallel box inside the unit cube that does not intersect with the point set. We study the expected dis…