20 citations · 51 across the 12 of their papers we have counts for
8 papers · 1 filter
Constructive discretization and approximation in reproducing kernel Hilbert spaces
Abdellah Chkifa, Matthieu Dolbeault, David Krieg +1
We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequal…
Approximation of Functions: Optimal Sampling and Complexity
David Krieg, Mario Ullrich
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numer…
Noisy nonlinear information and entropy numbers
David Krieg, Erich Novak, Leszek Plaskota +1
It is impossible to recover a vector from with less than linear measurements, even if the measurements are chosen adaptively. Recently, it has been shown that on…
Sparse grids vs. random points for high-dimensional polynomial approximation
Jakob Eggl, Elias Mindlberger, Mario Ullrich
We study polynomial approximation on a -cube, where is large, and compare interpolation on sparse grids, aka Smolyak's algorithm (SA), with a simple least squares method bas…
How many continuous measurements are needed to learn a vector?
David Krieg, Erich Novak, Mario Ullrich
One can recover vectors from with arbitrary precision, using only continuous measurements that are chosen adaptively. This surprising res…
On the power of adaption and randomization
David Krieg, Erich Novak, Mario Ullrich
We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are…
On the power of iid information for linear approximation
Mathias Sonnleitner, Mario Ullrich
This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functi…
Function values are enough for -approximation: Part II
David Krieg, Mario Ullrich
In the first part we have shown that, for -approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are…