23 citations · 64 across the 21 of their papers we have counts for
18 papers · 1 filter
Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres
Wolfgang Erb, Thomas Hangelbroek, Francis J. Narcowich +2
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis…
Krylov subspace methods to accelerate kernel machines on graphs
Wolfgang Erb
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-b…
Interpolation with the polynomial kernels
Giacomo Elefante, Wolfgang Erb, Francesco Marchetti +3
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are r…
On Kosloff Tal-Ezer Least-Squares Quadrature Formulas
Giacomo Cappellazzo, Wolfgang Erb, Francesco Marchetti +1
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is…
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction
Gaël Bringout, Wolfgang Erb, Jürgen Frikel
We derive a new 3D model for magnetic particle imaging (MPI) that is able to incorporate realistic magnetic fields in the reconstruction process. In real MPI scanners, the generate…
Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
Stefano De Marchi, Wolfgang Erb, Francesco Marchetti +2
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study…
Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk
Wolfgang Erb
Rhodonea curves are classical planar curves in the unit disk with the characteristic shape of a rose. In this work, we use point samples along such rose curves as node sets for a n…
A spectral interpolation scheme on the unit sphere based on the nodes of spherical Lissajous curves
Wolfgang Erb
For sampling values along spherical Lissajous curves we establish a spectral interpolation and quadrature scheme on the sphere. We provide a mathematical analysis of spherical Liss…
Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging
Wolfgang Erb, Andreas Weinmann, Mandy Ahlborg +10
Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response i…
A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb
The goal of this article is to provide a general multivariate framework that synthesizes well-known non-tensorial polnomial interpolation schemes on the Padua points, the Morrow-Pa…
Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb, Yurii Kolomoitsev +1
To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue c…
Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After clas…
Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case
Wolfgang Erb
In this article, we study bivariate polynomial interpolation on the node points of degenerate Lissajous figures. These node points form Chebyshev lattices of rank and are gener…
Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves
Wolfgang Erb, Christian Kaethner, Mandy Ahlborg +1
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization…
On adaptive discretization schemes for the regularization of ill-posed problems with semiiterative methods
Wolfgang Erb, Evgeniya V. Semenova
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that…
An alternative to Slepian functions on the unit sphere - A space-frequency analysis based on localized spherical polynomials
Wolfgang Erb, Sonja Mathias
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is c…
Accelerated Landweber methods based on co-dilated orthogonal polynomials
Wolfgang Erb
In this article, we introduce and study accelerated Landweber methods for linear ill-posed problems obtained by an alteration of the coefficients in the three-term recurrence relat…
Optimally space localized polynomials with applications in signal processing
Wolfgang Erb
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in term…