Preprints

• Craig Gross, Mark A. Iwen, Lutz Kämmerer, Toni Volkmer.
  Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables.
  ArXiv e-prints, 2020, arXiv:2012.09889 [math.NA]. (arXiv, pdf).
• Kai Bergermann, Martin Stoll, Toni Volkmer.
  Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products.
  ArXiv e-prints, 2020, arXiv:2007.05239 [math.NA]. (arXiv, pdf).
• Lutz Kämmerer, Felix Krahmer, Toni Volkmer.
  A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions.
  ArXiv e-prints, 2020, arXiv:2006.13053 [math.NA]. (arXiv, pdf).
• Craig Gross, Mark A. Iwen, Lutz Kämmerer, Toni Volkmer.
  A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size.
  ArXiv e-prints, 2020, arXiv:2003.09753 [math.NA]. (arXiv, pdf).
• Lutz Kämmerer, Tino Ullrich, Toni Volkmer.
  Worst case recovery guarantees for least squares approximation using random samples.
  ArXiv e-prints, 2019, arXiv:1911.10111 [math.NA]. (arXiv, pdf).
• Bosu Choi, Mark Iwen, Toni Volkmer.
  Sparse Harmonic Transforms II: Best s-Term Approximation Guarantees for Bounded Orthonormal Product Bases in Sublinear-Time.
  ArXiv e-prints, 2019; arXiv:1909.09564 [math.NA]. (arXiv, pdf).

Papers

• Lutz Kämmerer, Daniel Potts, Toni Volkmer.
  High-dimensional sparse FFT based on sampling along multiple rank-1 lattices.
  Appl. Comput. Harm. Anal. 51, 225 – 257, 2021. (arXiv, preprint, DOI).
• Lutz Kämmerer, Toni Volkmer.
  Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices.
  Journal of Approximation Theory (2019). (pdf, DOI).
• Dominik Alfke, Daniel Potts, Martin Stoll, Toni Volkmer.
  NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks.
  Front. Appl. Math. Stat. 4:61, 2018. (pdf, DOI).
• Glenn Byrenheid, Lutz Kämmerer, Tino Ullrich, Toni Volkmer.
  Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness.
  Numer. Math. 136, 993 – 1034, 2017. (pdf, DOI).
• Daniel Potts, Toni Volkmer.
  Multivariate sparse FFT based on rank-1 Chebyshev lattice sampling.
  2017 International Conference on Sampling Theory and Applications (SampTA), 504 – 508, 2017. (pdf, DOI).
• Daniel Potts, Manfred Tasche, Toni Volkmer.
  Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT.
  Front. Appl. Math. Stat. 2, Article 1, 2016. (pdf, DOI).
• Daniel Potts, Toni Volkmer.
  Sparse high-dimensional FFT based on rank-1 lattice sampling.
  Appl. Comput. Harm. Anal. 41, 713 – 748, 2016. (pdf, DOI, related software).
• Daniel Potts, Toni Volkmer.
  Fast and exact reconstruction of arbitrary multivariate algebraic polynomials in Chebyshev form.
  Proceedings of the 11th International Conference on Sampling Theory and Applications, 392 – 396, 2015.
  (pdf, extended preprint, DOI).
• Lutz Kämmerer, Daniel Potts, Toni Volkmer.
  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. (pdf, DOI).
• Lutz Kämmerer, Daniel Potts, Toni Volkmer.
  Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling.
  J. Complexity 31, 543 – 576, 2015. (pdf, extended preprint, DOI).
• Toni Volkmer.
  Taylor and rank-1 lattice based nonequispaced fast Fourier transform.
  In 10th international conference on Sampling Theory and Applications (SampTA 2013), pages 576 – 579, Bremen, Germany, July 2013. (pdf, DOI).
• Jochen Strunk, Toni Volkmer, Wolfgang Rehm, Heiko Schick.
  Design and Performance of a Grid of Asynchronously Clocked Run-Time Reconfigurable Modules on a FPGA.
  In International Conference on Reconfigurable Computing and FPGAs (RECONFIG 2009), pages 392 – 397, Cancun, Mexico, December 2009.
• Jochen Strunk, André Heinig, Toni Volkmer, Wolfgang Rehm, Heiko Schick.
  ACCFS – Virtual File System Support for Host Coupled Run-Time Reconfigurable FPGAs.
  In International Conference on Parallel Computing (ParCo 2009), pages 632 – 639, Lyon, France, September 2009.
• Jochen Strunk, Toni Volkmer, Wolfgang Rehm, Heiko Schick.
  An on Chip Network inside a FPGA for Run-Time Reconfigurable Low Latency Grid Communication.
  In Euromicro Conference on Digital System Design (DSD 2009), Patras, Greece, August 2009.
• Jochen Strunk, Toni Volkmer, Klaus Stephan, Wolfgang Rehm, Heiko Schick.
  Impact of Run-Time Reconfiguration on Design and Speed – A Case Study Based on a Grid of Run-Time Reconfigurable Modules inside a FPGA.
  In IEEE International Symposium on Parallel & Distributed Processing 2009 (IPDPS 2009), Rome, Italy, May 2009.
• Jochen Strunk, André Heinig, Toni Volkmer, Wolfgang Rehm, Heiko Schick.
  Run-Time Reconfiguration for HyperTransport coupled FPGAs using ACCFS.
  In First International Workshop on HyperTransport Research and Applications (WHTRA), pages 54 – 63, Mannheim, Germany, February 2009.

Others

• Toni Volkmer.
  

  Multivariate Approximation and High-Dimensional Sparse FFT Based on Rank-1 Lattice Sampling. Dissertation (PhD thesis), Faculty of Mathematics, Technische Universität Chemnitz (Chemnitz University of Technology), 2017. (permalink, pdf). Published at Universitätsverlag der Technischen Universität Chemnitz, ISBN 978-3-96100-020-3, 2017.

• Toni Volkmer.
  OpenMP parallelization in the NFFT software library.
  Technische Universität Chemnitz, Fakultät für Mathematik, Preprint 7, 2012. (pdf).