4 citations · 18 across the 13 of their papers we have counts for
5 papers · 1 filter
The power of random information for numerical approximation and integration
Mathias Sonnleitner
This thesis investigates the quality of randomly collected data by employing a framework built on information-based complexity, a field related to the numerical analysis of abstrac…
Function recovery on manifolds using scattered data
David Krieg, Mathias Sonnleitner
We consider the task of recovering a Sobolev function on a connected compact Riemannian manifold when given a sample on a finite point set. We prove that the quality of the sam…
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…
On the relation of the spectral test to isotropic discrepancy and -approximation in Sobolev spaces
Mathias Sonnleitner, Friedrich Pillichshammer
This paper is a follow-up to the recent paper "A note on isotropic discrepancy and spectral test of lattice point sets" [J. Complexity, 58:101441, 2020]. We show that the isotropic…
Random points are optimal for the approximation of Sobolev functions
David Krieg, Mathias Sonnleitner
We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space on bo…