47 citations · 245 across the 29 of their papers we have counts for
33 papers
Optimal Algorithms for Numerical Integration: Recent Results and Open Problems
Erich Novak
We present recent results on optimal algorithms for numerical integration and several open problems. The paper has six parts: 1. Introduction 2. Lower Bounds 3. Universality 4. Gen…
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…
Lower bounds for integration and recovery in
Aicke Hinrichs, David Krieg, Erich Novak +1
Function values are, in some sense, "almost as good" as general linear information for -approximation (optimal recovery, data assimilation) of functions from a reproducing ker…
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 $…
Algorithms and Complexity for Functions on General Domains
Erich Novak
Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a…
On the power of random information
Aicke Hinrichs, David Krieg, Erich Novak +2
We study approximation and integration problems and compare the quality of optimal information with the quality of random information. For some problems random information is almos…