research
∙
06/30/2023
On numerical realizations of Shannon's sampling theorem
In this paper, we discuss some numerical realizations of Shannon's sampl...
share
research
∙
06/15/2023
ANOVA approximation with mixed tensor product basis on scattered points
In this paper we consider an orthonormal basis, generated by a tensor pr...
research
∙
03/31/2023
Optimal density compensation factors for the reconstruction of the Fourier transform of bandlimited functions
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algori...
research
∙
02/01/2023
Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform
The well-known discrete Fourier transform (DFT) can easily be generalize...
research
∙
11/11/2022
Nonlinear approximation in bounded orthonormal product bases
We present a dimension-incremental algorithm for the nonlinear approxima...
research
∙
08/29/2022
On the reconstruction of functions from values at subsampled quadrature points
This paper is concerned with function reconstruction from samples. The s...
research
∙
07/26/2022
Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation
We use hyperbolic wavelet regression for the fast reconstruction of high...
research
∙
03/18/2022
On regularized Shannon sampling formulas with localized sampling
In this paper we present new regularized Shannon sampling formulas which...
research
∙
10/14/2021
Interpretable transformed ANOVA approximation on the example of the prevention of forest fires
The distribution of data points is a key component in machine learning. ...
research
∙
09/09/2021
The uniform sparse FFT with application to PDEs with random coefficients
We develop an efficient, non-intrusive, adaptive algorithm for the solut...
research
∙
08/30/2021
Fast Hyperbolic Wavelet Regression meets ANOVA
We use hyperbolic wavelet regression for the fast reconstruction of high...
research
∙
07/06/2021
Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms
In this paper we study the nonuniform fast Fourier transform with nonequ...
research
∙
03/25/2021
Interpretable Approximation of High-Dimensional Data
In this paper we apply the previously introduced approximation method ba...
research
∙
02/01/2021
A note on transformed Fourier systems for the approximation of non-periodic signals
A variety of techniques have been developed for the approximation of non...
research
∙
10/20/2020
Grouped Transformations in High-Dimensional Explainable ANOVA Approximation
Many applications are based on the use of efficient Fourier algorithms s...
research
∙
10/14/2020
Continuous window functions for NFFT
In this paper, we study the error behavior of the nonequispaced fast Fou...
research
∙
12/20/2019
Uniform error estimates for the NFFT
In this paper, we study the error behavior of the known fast Fourier tra...
research
∙
12/06/2019
Learning multivariate functions with low-dimensional structures using polynomial bases
In this paper we study the multivariate ANOVA decomposition for function...
research
∙
12/06/2019
Efficient multivariate approximation on the cube
For the approximation of multivariate non-periodic functions h on the hi...
research
∙
07/26/2019
Learning high-dimensional additive models on the torus
In this paper we study the multivariate ANOVA decomposition for 1-period...
research
∙
08/14/2018