12 citations · 15 across the 7 of their papers we have counts for
10 papers
Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables
Craig Gross, Mark Iwen, Lutz Kämmerer +1
We consider fast, provably accurate algorithms for approximating functions on the -dimensional torus, , that are sparse (or compressibl…
Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products
Kai Bergermann, Martin Stoll, Toni Volkmer
We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs. Besides the treatment of various applicatio…
A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions
Lutz Kämmerer, Felix Krahmer, Toni Volkmer
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier ba…
A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size
Craig Gross, Mark A. Iwen, Lutz Kämmerer +1
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The…
Worst-case recovery guarantees for least squares approximation using random samples
Lutz Kämmerer, Tino Ullrich, Toni Volkmer
We construct a least squares approximation method for the recovery of complex-valued functions from a reproducing kernel Hilbert space on . The nodes are dr…
Sparse Harmonic Transforms II: Best -Term Approximation Guarantees for Bounded Orthonormal Product Bases in Sublinear-Time
Bosu Choi, Mark Iwen, Toni Volkmer
In this paper, we develop a sublinear-time compressive sensing algorithm for approximating functions of many variables which are compressible in a given Bounded Orthonormal Product…
NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks
Dominik Alfke, Daniel Potts, Martin Stoll +1
The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network an…
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…
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…