2 citations · 4 across the 6 of their papers we have counts for
8 papers
Constructing efficient spatial discretizations of spans of multivariate Chebyshev polynomials
Lutz Kämmerer
For an arbitrary given span of high-dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampl…
Nonlinear approximation in bounded orthonormal product bases
Lutz Kämmerer, Daniel Potts, Fabian Taubert
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect…
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…
The uniform sparse FFT with application to PDEs with random coefficients
Lutz Kämmerer, Daniel Potts, Fabian Taubert
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with rando…
Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices
Lutz Kämmerer, Toni Volkmer
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing m…
High-dimensional sparse FFT based on sampling along multiple rank-1 lattices
Lutz Kämmerer, Daniel Potts, Toni Volkmer
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast…
Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform
Lutz Kämmerer
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonomet…
Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness
Glenn Byrenheid, Lutz Kämmerer, Tino Ullrich +1
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank- integration lattice. The main result is the fact…