4 citations · 13 across the 11 of their papers we have counts for
10 papers · 1 filter
Required Number of Points in Marcinkiewicz-Zygmund Inequalities
Felix Bartel
We determine, up to absolute constants, the worst-case number of point evaluations required for a weighted Marcinkiewicz-Zygmund inequality for an -dimensional complex fun…
Exact discretization, tight frames and recovery via D-optimal designs
Felix Bartel, Lutz Kämmerer, Kateryna Pozharska +2
-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants…
Efficient recovery of non-periodic multivariate functions from few scattered samples
Felix Bartel, Kai Lüttgen, Nicolas Nagel +1
It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate funct…
Nonlinear Approximation with Subsampled Rank-1 Lattices
Felix Bartel, Fabian Taubert
In this paper we approximate high-dimensional functions by sparse trigonometric polynomials based on function evaluations. Recently it was shown th…
On the reconstruction of functions from values at subsampled quadrature points
Felix Bartel, Lutz Kämmerer, Daniel Potts +1
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) un…
Error Guarantees for Least Squares Approximation with Noisy Samples in Domain Adaptation
Felix Bartel
Given samples of a function in random points drawn with respect to a measure we develop theoretical analysis of the -appr…
Constructive subsampling of finite frames with applications in optimal function recovery
Felix Bartel, Martin Schäfer, Tino Ullrich
In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in . Based on a suitable random subsampling…
Concentration Inequalities for Cross-validation in Scattered Data Approximation
Felix Bartel, Ralf Hielscher
Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare…
Grouped Transformations and Regularization in High-Dimensional Explainable ANOVA Approximation
Felix Bartel, Daniel Potts, Michael Schmischke
In this paper we propose a tool for high-dimensional approximation based on trigonometric polynomials where we allow only low-dimensional interactions of variables. In a general hi…
Fast Cross-validation in Harmonic Approximation
Felix Bartel, Ralf Hielscher, Daniel Potts
Finding a good regularization parameter for Tikhonov regularization problems is a though yet often asked question. One approach is to use leave-one-out cross-validation scores to i…