Preprints

  • Erb, W., Hangelbroek, T., and Ron, A. Anisotropic Gaussian approximation in $L_2(\mathbb{R}^2)$. arXiv:1910.10319 (2019) (Preprint)
  • Erb, W. Shapes of Uncertainty in Spectral Graph Theory. arXiv:1909.10865 (2019) (Preprint) (Software GUPPY)
  • De Marchi, S., Erb, W., Marchetti, F., Perracchione, E. and Rossini, M. Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI. arXiv:1903.03095 (2019) (Preprint) (Poster)
  • Erb, W. Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk. Constr. Approx. (accepted for publication) (2019) (Preprint) (Software RDisk) (Rhodonea curves) (Poster)
  • Erb, W. A spectral interpolation scheme on the unit sphere based on the nodes of spherical Lissajous curves. IMA J. Numer. Anal. (accepted for publication) (2019) (Preprint) (Software LSphere) (Spherical Lissajous curves)
  • Erb, W. Weak limits for weighted means of orthogonal polynomials. J. Spectral Theory (accepted for publication) (2019) (Preprint)
  • Dencker, P. and Erb, W. A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes. arXiv:1711.00557 (2017) (Preprint) (Software 2D) (Software 3D) (Slides) (LC2Dfevalapp) (LC2Dplotapp)

2018

  • Erb, W., Weinmann, A., Ahlborg, M., Brandt, C., Bringout, G. , Buzug, T.M, Frikel J., Kaethner, C., Knopp, T., März, T., Möddel, M., Storath, M. and Weber, A. Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging. Inverse Problems 34 (2018), 055012 (Preprint) (Slides)

2017

  • Dencker, P., Erb, W., Kolomoitsev, Y. and Lomako, T. Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes. Journal of Complexity 43, (2017), 1-27 (Preprint)
  • Dencker, P. and Erb, W. Multivariate polynomial interpolation on Lissajous-Chebyshev nodes. J. Approx. Theory 219 (2017), 15-45 (Preprint) (Software) (Slides)
  • Schmiester, L., Moddel, M., Erb, W. and Knopp, T. Direct Image Reconstruction of Lissajous Type Magnetic Particle Imaging Data using Chebyshev-based Matrix Compression. IEEE Transactions on Computational Imaging 3:4 (2017), 671-681
  • De Marchi, S., Erb, W. and Marchetti, F. Spectral filtering for the reduction of the Gibbs phenomenon for polynomial approximation methods on Lissajous curves with applications in MPI. Dolomites Res. Notes Approx. 10 (2017), 128-137 (Publication)
  • De Marchi, S., Erb, W. and Marchetti, F. Lissajous sampling and spectral filtering in MPI applications: the reconstruction algorithm for reducing the Gibbs phenomenon. 2017 International Conference on Sampling Theory and Applications (SampTA) (2017), 580-584

2016

  • Kaethner, C., Erb, W., Ahlborg, M., Szwargulski, P., Knopp, T. and Buzug, T. M. Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging based on Lissajous Node Points. IEEE Transactions on Medical Imaging 35:11 (2016), 2476-2485
  • Erb, W. Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case. Appl. Math. Comput. 289 (2016), 409-425 (Preprint)
  • Erb, W., Kaethner, C., Ahlborg, M. and Buzug, T.M. Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves. Numer. Math. 133:4 (2016), 685-705 (Preprint) (Software)

2015

  • Erb, W., Kaethner, C., Dencker, P., and Ahlborg, M. A survey on bivariate Lagrange interpolation on Lissajous nodes. Dolomites Research Notes on Approximation 8 (Special issue) (2015), 23-36 (Publication) (Software)
  • Erb, W. und Semenova, E.V. On adaptive discretization schemes for the solution of ill-posed problems with semiiterative methods. Appl. Anal. 94:10 (2015), 2057-2076 (Preprint)
  • Erb, W. und Mathias, S. An alternative to Slepian functions on the unit sphere - A space-frequency analysis based on localized spherical polynomials. Appl. Comput. Harmon. Anal. 38:2 (2015), 222-241 (Preprint)
  • Erb, W. Accelerated Landweber methods based on co-dilated orthogonal polynomials. Numer. Alg. 68:2 (2015), 229-260 (Preprint)

2013

  • Erb, W. An orthogonal polynomial analogue of the Landau-Pollak-Slepian time-frequency analysis. J. Approx. Theory 166 (2013), 56-77 (Preprint)

2012

  • Erb, W. Optimally space localized polynomials with applications in signal processing. J. Fourier Anal. Appl. 18:1 (2012), 45-66 (Preprint)

2011

  • Erb, W., and Toókos, F. Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems. Appl. Math. Comput. 217:9 (2011), 4771-4780 (Preprint)

2010

  • Erb, W. Uncertainty principles on compact Riemannian manifolds. Appl. Comput. Harmon. Anal. 29:2 (2010), 182-197 (Preprint)
  • Erb, W. Uncertainty principles on Riemannian manifolds. TU München, Dissertation

2008

  • Erb, W., and Filbir, F. Approximation by positive definite functions on compact groups. Numer. Funct. Anal. Optim. 29:9-10 (2008), 1082-1107 (Preprint)