33 citations · 157 across the 27 of their papers we have counts for
6 papers · 1 filter
Uniform error estimates for nonequispaced fast Fourier transforms
Daniel Potts, Manfred Tasche
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly su…
Learning multivariate functions with low-dimensional structures using polynomial bases
Daniel Potts, Michael Schmischke
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An importan…
Efficient multivariate approximation on the cube
Robert Nasdala, Daniel Potts
We combine a periodization strategy for weighted -integrands with efficient approximation methods in order to approximate multivariate non-periodic functions on the high-dim…
Approximation of high-dimensional periodic functions with Fourier-based methods
Daniel Potts, Michael Schmischke
In this paper we propose an approximation method for high-dimensional -periodic functions based on the multivariate ANOVA decomposition. We provide an analysis on the classical…
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…
A sparse FFT approach for ODE with random coefficients
Maximilian Bochmann, Lutz Kämmerer, Daniel Potts
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The…