Preprints

• Kämmerer, L., Potts, D., Taubert, F.
  The uniform sparse FFT with application to PDEs with random coefficients .
  ArXiv e-prints, 2021, arXiv:arXiv:2109.04131 [math.NA] (arXiv).
• Kämmerer, L.
  A fast probabilistic component-by-component construction of exactly integrating rank-1 lattices and applications.
  ArXiv e-prints, 2020, arXiv:2012.14263 [math.NA] (arXiv).
• Kämmerer, L.
  Multiple Lattice Rules for Multivariate L_∞ Approximation in the Worst-Case Setting.
  ArXiv e-prints, 2019; arXiv:1909.02290 [math.NA] (arXiv).

Publications

• Gross, C., Iwen, M.A., Kämmerer, L., Volkmer, T.
  Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables.
  Sampl. Theory Signal Process. Data Anal. 20, 1, 2022, doi:10.1007/s43670-021-00018-y (arXiv).
• Kämmerer, L., Krahmer, F., Volkmer, T.
  A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions.
  Numer. Algor. 89, 1479-1520, 2022, doi:10.1007/s11075-021-01162-1 (Open Access).
• Gross, C., Iwen, M. A., Kämmerer, L., Volkmer, T.
  A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size.
  Adv. Comput. Math. 47, 86, 2021 (arXiv).
• Kämmerer, L., Ullrich, T., Volkmer, T.
  Worst case recovery guarantees for least squares approximation using random samples.
  Constr. Approx. 54, 295-352, 2021 (Open Access).
• Kämmerer, L., Potts, D., Volkmer, T.
  High-dimensional sparse FFT based on sampling along multiple rank-1 lattices.
  Appl. Comput. Harmon. Anal. 51, 225-257, 2021, doi:10.1016/j.acha.2020.11.002 (arXiv).
• Bochmann, M., Kämmerer, L., Potts, D.
  A sparse FFT approach for ODE with random coefficients.
  Adv. Comput. Math. 46, 65, 2020, (Open Access).
• Kämmerer, L., Volkmer, T.
  Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices.
  J. Approx. Theory 246, 1-27, 2019, doi:10.1016/j.jat.2019.05.001 (arXiv).
• Kämmerer, L.
  Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform.
  Appl. Comput. Harmon. Anal. 47, 702-729, 2019, doi:10.1016/j.acha.2017.11.008. (arXiv).
• Byrenheid, G., Kämmerer, L., Ullrich, T., Volkmer, T.
  Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness.
  Numer. Math., 2017, doi:10.1007/s00211-016-0861-7. (pdf).
• Kämmerer, L.
  Multiple Rank-1 Lattices as Sampling Schemes for Multivariate Trigonometric Polynomials. 
  J. Fourier Anal. Appl., 2016, doi:10.1007/s00041-016-9520-8. (pdf).
• Kämmerer, L., Potts, D., Volkmer, T.
  Approximation of multivariate functions by trigonometric polynomials based on rank-1 lattice sampling.
  J. Complexity 31, 543-576, 2015. (full paper pdf, extended Preprint)
• Kämmerer, L., Potts, D., Volkmer, T.
  Approximation of multivariate periodic functions by trigonometric polynomials based on sampling along rank-1 lattice with generating vector of Korobov form.
  J. Complexity 31, 424-456, 2015. (full paper pdf)
• Kämmerer, L., Kunis, S., Melzer, I., Potts, D., Volkmer, T.
  Computational Methods for the Fourier Analysis of Sparse High-Dimensional Functions.
  in: Extraction of Quantifiable Information from Complex Systems, S. Dahlke, W. Dahmen, M. Griebel, W. Hackbusch, K. Ritter, R. Schneider, C. Schwab, H. Yserentant (Eds.), Springer International Publishing, 347-363, 2014. (full paper pdf)
• Kämmerer, L.
  Reconstructing Multivariate Trigonometric Polynomials from Samples Along Rank-1 Lattices
  in: Approximation Theory XIV: San Antonio 2013 , G.E. Fasshauer and L.L. Schumaker (Eds.), Springer International Publishing, 255-271, 2014. (full paper pdf)
• Kämmerer, L.
  Reconstructing Hyperbolic Cross Trigonometric Polynomials by Sampling along Rank-1 Lattices
  SIAM J. Numer. Anal. 51, 2773-2796, 2013. (full paper pdf)
• Kämmerer, L.
  Reconstructing Multivariate Trigonometric Polynomials by Sampling along Generated Sets
  in: Monte Carlo and Quasi-Monte Carlo Methods 2012, J. Dick, F.Y. Kuo, G.W. Peters, and I.H. Sloan (Eds.), Springer-Verlag, Berlin, 439-454, 2013. (full paper pdf)
• Kämmerer, L., Kunis, S., and Potts, D.
  Interpolation lattices for hyperbolic cross trigonometric polynomials
  J. Complexity 28, 76-92, 2012. (full paper pdf)
• Kämmerer, L. and Kunis, S.
  On the stability of the hyperbolic cross discrete Fourier transform
  Numer. Math. 117, 581-600, 2011. (full paper pdf)

Others

• Kämmerer, L.
  High Dimensional Fast Fourier Transform Based on Rank-1 Lattice Sampling
  Dissertation (PhD thesis), 2014. (pdf)