Navigation

Inhalt Hotkeys
Professur für Angewandte Funktionalanalysis
Professur für Angewandte Funktionalanalysis

Papers and Citations in google scholar

Papers on ORCiD

Preprint

o Bartel, F., Hielscher, R., Potts, D. Fast Cross-validation in Harmonic Analysis. arXiv:1901.10206   (full paper pdf)   2019
o Bochmann, M., Kämmerer, L., Potts, D. A sparse FFT approach for ODE with random coefficients. arXiv:1901.01600   (full paper pdf)   2019
o Nasdala, R., Potts, D. Transformed Rank-1 Lattices for high-dimensional approximation. arXiv:1805.09106   (full paper pdf)   2018
o Kämmerer, L., Potts, D., Volkmer, T. High-dimensional sparse FFT based on sampling along multiple rank-1 lattices. arXiv:1711.05152   (full paper pdf)   2017

Book

o o Plonka, G., Potts, D., Steidl, G.,Tasche, M.
Numerical Fourier Analysis.
ANHA, Birkhäuser, ISBN 978-3-030-04305-6
Slides for flipped classroom lectures:
lecture course I, based on Chapter 1, 2, 3, 5, 7
lecture course II, based on Chapter 4, 8, 9,10
This book is available via springer or springer-online.

Papers in Journals

o Kircheis, M., Potts, D. Direct inversion of the nonequispaced fast Fourier transform. Linear Algebra Appl., accepted, arXiv:1811.05335   (full paper pdf)   2019
o Weeber, R., Nestler, F., Weik, F., Pippig, M., Potts, D., Holm C. Accelerating the calculation of dipolar interactions in particle based simulations with open boundary conditions by means of the P2NFFT method. J. Comput. Phys., accepted, arXiv:1808.10341   (full paper pdf)   2019
o Alfke, D., Potts, D., Stoll M., Volkmer, T. NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Front. Appl. Math. Stat. (Section: Mathematics of Computation and Data Science), 4:61,   arXiv:1808.04580   (full paper pdf, Frontiers, related software),   2018
o Potts, D., Tasche, M., Volkmer, T. Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT. Front. Appl. Math. Stat. (Section: Mathematics of Computation and Data Science), 2:1,   (full paper pdf, Frontiers, related software),   2016
o Potts, D., Tasche, M. Reconstruction of sparse Legendre and Gegenbauer expansions. BIT 56, 1019-1043,   (full paper pdf),   2016
o Junghanns, P., Kaiser, R., Potts, D. Collocation–quadrature methods and fast summation for Cauchy singular integral equations with fixed singularities. Linear Algebra Appl. 491, 187-238,   (full paper pdf),   2016
o Potts, D., Volkmer, T. Sparse high-dimensional FFT based on rank-1 lattice sampling. Appl. Comput. Harm. Anal. 41, 713-748,   (full paper pdf, DOI, related software),   2016
o Kämmerer, L., Potts, D., Volkmer, T. Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling. J. Complexity 31, 543-576,   (full paper pdf, extended Preprint),   2015
o Nestler, F., Pippig, M., Potts, D. Fast Ewald Summation based on NFFT with Mixed Periodicity. J. Comput. Phys. 285, 280-315,   (full paper pdf),   2015
o Potts, D., Tasche, M. Fast ESPRIT algorithms based on partial singular value decompositions. Appl. Numer. Math. 88, 31-45,   (full paper pdf, ApplNumerMath_PDF),   2015
o 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,   (full paper pdf),   2015
o Potts, D., Tasche, M. Sparse polynomial interpolation in Chebyshev bases. Linear Algebra Appl. 441, 61-87,   (full paper pdf, LAA_PDF),   2014
o Arnold, A., Bolten, M., Dachsel, H., Fahrenberger, F., Gähler, F., Halver, R. Heber, F., Hofmann, M., Holm, C., Iseringhausen, J., Kabadshow, I., Lenz, O., Pippig, M., Potts, D. Sutmann, G. A Comparison of Scalable Fast Methods for Long-Range Interactions. Phys. Rev. E, 88, 063308,   (full paper pdf),   2013
o Pippig, M., Potts, D. Parallel Three-Dimensional Nonequispaced Fast Fourier Transforms and Their Application to Particle Simulation. SIAM J. Sci. Comput., 35, C411-C437   (full paper pdf),   2013
o Potts, D., Tasche, M. Parameter estimation for multivariate exponential sums. Electron. Trans. Numer. Anal., 40, 204-224   (full paper pdf),   2013
o Potts, D., Tasche, M. Parameter estimation for nonincreasing exponential sums by Prony-like methods. Linear Algebra Appl. 439, 1024-1039,   (full paper pdf),   2013
o Gräf, M., Potts, D., Steidl, G. Quadrature rules, discrepancies and their relations to halftoning on the torus and the sphere. SIAM J. Sci. Comput. 34, A2760-A2791,   (full paper pdf, see also Quadrature rules on manifolds),   2012
o Kämmerer, L., Kunis, S., Potts, D. Interpolation lattices for hyperbolic cross trigonometric polynomials. J. Complexity 28, 76-92,   (full paper pdf),   2012
o Gräf, M., Potts, D. On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms. Numer. Math. 119, 699-724, (full paper pdf, see also Quadrature rules on manifolds),   2011
o Peter, T., Potts, D., Tasche M. Nonlinear approximation by sums of exponentials and translates. SIAM J. Sci. Comput. 33, 1920-1947,   (full paper pdf),   2011
o Backofen, R., Gräf, M., Potts, D., Praetorius, S., Voigt, A., Witkowski, T. A continuous approach to discrete ordering on S^2. Multiscale Model. Simul. 9, 314-334,   (full paper pdf),   2011
o Potts, D., Tasche M. Nonlinear approximation by sums of nonincreasing exponentials. Appl. Anal. 90, 609-626,   (full paper ps, pdf),   2011
o Filbir, F., Potts, D. Scattered data approximation on the bi-sphere and application to texture analysis. Math. Geosci. 42, 747-771,   (full paper ps, pdf, Proof of Theorem 4.5 ),   2010
o Döhler, M., Kunis, S., Potts, D. Nonequispaced hyperbolic cross fast Fourier transform. SIAM J. Numer. Anal. 47, 4415-4428,   (full paper ps, pdf),   2010
o Potts, D., Tasche M. Parameter estimation for exponential sums by approximate Prony method. Signal Process. 90, 1631-1642,   (full paper ps, pdf),   2010
o Potts, D., Prestin J., Vollrath A. A Fast algorithm for nonequispaced Fourier transforms on the rotation group. Numer. Algorithms, 52, 355 - 384,   (full paper ps, pdf),   2009
o Keiner, J., Kunis, S., Potts, D. Using NFFT 3 - a software library for various nonequispaced fast Fourier transforms ACM Trans. Math. Software, 36, Article 19, 1-30,   (full paper ps, pdf)   2009
o Gräf, M., Potts, D. Sampling sets and quadrature formulae on the rotation group. Numer. Funct. Anal. Optim. 30, 665-688,   (full paper ps, pdf),   2009
o Gräf, M., Kunis, S., Potts, D. On the computation of nonnegative quadrature weights on the sphere. Appl. Comput. Harm. Anal. 27, 124-132,   (full paper ps, pdf),   2009
o Böttcher, A., Kunis, S., Potts, D. Probabilistic spherical Marcinkiewicz-Zygmund inequalities. J. Approx. Theory 157, 113-126,   (full paper ps, pdf),   2009
o Hielscher, R., Potts, D., Prestin, J., Schaeben, H., Schmalz, M. The Radon transform on SO(3): A Fourier slice theorem and numerical inversion. Inverse Problems 24, 025011,   (full paper ps, pdf),   2008
o Kunis, S., Potts, D. Time and memory requirements of the Nonequispaced FFT. Sampling Theory in Signal and Image Processing 7, 77-100,   (full paper ps, pdf),   2008
o Potts, D., Tasche, M. Numerical stability of nonequispaced fast Fourier transforms. J. Comput. Appl. Math. 222, 655-674,   (full paper ps, pdf),   2008
o Keiner, J., Potts, D. Fast evaluation of quadrature formulae on the sphere. Math. Comput. 77, 397-419,   (full paper ps, pdf),   2008
o Schaeben, H., Hielscher, R., Fundenberger, J.J.,Potts, D., Prestin, J. Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers. J. Appl. Cryst. 40, 570-579.   (full paper ps, pdf),   2007
o Keiner, J., Kunis, S., Potts, D. Efficient reconstruction of functions on the sphere from scattered data. J. Fourier Anal. Appl. 13, 435-458.   (full paper ps, pdf),   2007
o Böttcher, A., Potts, D. Probability against condition number and sampling of multivariate trigonometric random polynomials. Electron. Trans. Numer. Anal. 26, 178-189.   (full paper ps, pdf),   2007
o Böttcher, A., Potts, D., Wenzel, D A probability argument in favor of ignoring small singular values. Operators and Matrices 1, 31-43.   (full paper ps, pdf),   2007
o Knopp, T., Kunis, S., Potts, D. A note on the iterative MRI reconstruction from nonuniform k-space data. Int. J. Biomed. Imag , 2007, ID 24727   (full paper ps, pdf, webpage)   2007
o Kunis, S., Potts, D. Stability Results for Scattered Data Interpolation by Trigonometric Polynomials. SIAM J. Sci. Comput. 29, 1403 - 1419,   (full paper ps, pdf)   2007
o Fenn, M., Kunis, S., Potts, D. On the computation of the polar FFT. Appl. Comput. Harm. Anal. 22, 257-263,   (full paper ps, pdf),   2007
o Eggers, H., Knopp, T., Potts, D. Field Inhomogeneity Correction based on Gridding Reconstruction for Magnetic Resonance Imaging. IEEE Trans. Med. Imag. 26, 374-384,   (full paper ps, pdf, poster),   2007
o Keiner, J., Kunis, S., Potts, D. Fast summation of radial functions on the sphere. Computing 78, 1-15.   (full paper ps, pdf),   2006
o Kunis, S., Potts, D., Steidl, G. Fast Gauss transforms with complex parameters using NFFTs. J. Numer. Math. 14, 295-303.   (full paper ps, pdf),   2006
o Fenn, M., Kunis, S., Potts, D. Fast evaluation of trigonometric polynomials from hyperbolic crosses. Numer. Algorithms 41, 339-252. (full paper ps, pdf),   2006
o Fenn, M., Potts, D. Fast summation based on fast trigonometric transforms at nonequispaced nodes. Numer. Linear Algebra Appl. 12, 161-169. (full paper ps, pdf),   2005
o Potts, D., Steidl, G., Nieslony, A. Fast convolution with radial kernels at nonequispaced knots. Numer. Math. 98, 329-351. (full paper ps, pdf),   2004
o Potts, D. Approximation of scattered data by trigonometric polynomials on the torus and the 2-sphere. Adv. Comput. Math. 21, 21-36. (full paper ps.Z, pdf),   2004
o Böhme, M., Potts, D. A fast algorithm for filtering and wavelet decomposition on the sphere. Electron. Trans. Numer. Anal. 16, 70-92. (full paper ps, pdf),   2003
o Kunis, S., Potts, D. Fast spherical Fourier algorithms. J. Comput. Appl. Math. 161, 75-98. (full paper ps, pdf),   2003
o Potts, D., Steidl, G. Fast summation at nonequispaced knots by NFFTs. SIAM J. Sci. Comput. 24, 2013-2037. (full paper ps, pdf),   2003
o Potts, D. Fast algorithms for discrete polynomial transforms on arbitrary grids. Linear Algebra Appl. 366, 353-370. (full paper ps.Z, pdf),   2003
o Potts, D., Steidl, G., Tasche, M. Numerical stability of fast trigonometric transforms - a worst case study. J. Concrete Appl. Math. 1, 1-36. (full paper ps, pdf),   2002
o Potts, D., Steidl, G. Fourier reconstruction of functions from their nonstandard sampled Radon transform. J. Fourier Anal. Appl. 8, 513-533. (full paper ps, pdf),   2002
o Ng, M.K., Potts, D. Fast Iterative methods for Sinc systems. SIAM J. Matrix Anal. Appl. 24, 581-598. (full paper ps, pdf),   2002
o Ng, M. K., Potts, D. Circulant preconditioners for indefinite Toeplitz systems. BIT 41,1079-1088. (full paper ps, pdf),   2001
o Potts, D., Steidl, G. A new linogram algorithm for computerized tomography. IMA J. Numer. Anal. 21, 769-782. (full paper ps, pdf),   2001
o Potts, D., Steidl, G. Preconditioners for ill-conditioned Toeplitz matrices constructed from positive kernels. SIAM J. Sci. Comput. 22,1741-1761. (full paper ps.Z, pdf),   2001
o Chan, R., Potts, D., Steidl, G. Preconditioners for non-Hermitian Toeplitz systems. Numer. Linear Alg. Appl. 8,83-98. (full paper ps, pdf),   2001
o Chan, R., Potts, D., Steidl, G. Preconditioners for nondefinite Hermitian Toeplitz systems. SIAM J. Matrix Anal. Appl. 22,647-665. (full paper ps, pdf),   2000
o Potts, D., Steidl, G. Preconditioners for ill-conditioned Toeplitz matrices. BIT 39,513-533. (full paper ps.Z, pdf),   1999
o Potts, D., Steidl G., Tasche M. Fast algorithms for discrete polynomial transforms. Math. Comput. 67, 1577-1590. (full paper ps.Z, pdf),   1998
o Potts, D., Steidl G., Tasche M. Fast and stable algorithms for discrete spherical Fourier transforms. Linear Algebra Appl. 275, 433-450. (full paper ps.Z, pdf),   1998
o Potts, D., Steidl G. Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems. Linear Algebra Appl. 281, 265-292. (full paper ps.Z, pdf),   1998

Proceedings Papers and Book Chapters

o Hielscher, R., Potts D., Quellmalz M. An SVD in Spherical Surface Wave Tomography. In: Bernd Hofmann, Antonio Leitao and Jorge P. Zubelli (Eds.). New Trends in Parameter Identification for Mathematical Models, Birkhäuser Basel, 2018,   (full paper pdf, arXiv:1706.05284)   2017
o Potts, D., Van Buggenhout, N. Fourier extension and sampling on the sphere. Proceedings of the 12th International Conference on Sampling Theory and Applications, pages,   (full paper pdf ),   2017
o Potts, D., Volkmer, T. Multivariate sparse FFT based on rank-1 Chebyshev lattice sampling. Proceedings of the 12th International Conference on Sampling Theory and Applications, pages,   (full paper pdf ),   2017
o Potts, D., Tasche, M. Error estimates for the ESPRIT algorithm. Operator Theory: Advances and Applications, Vol. 259, Springer International Publishing, pages 621–648,   (full paper pdf),   2017
o Potts, D., Volkmer, T. Fast and exact reconstruction of arbitrary multivariate algebraic polynomials in Chebyshev form. Proceedings of the 11th International Conference on Sampling Theory and Applications, pages 392-396,   (full paper pdf, extended preprint ),   2015
o Nestler, F., Pippig, M., Potts, D. NFFT based fast Ewald summation for various types of periodic boundary conditions. in: Computational Trends in Solvation and Transport in Liquids, G. Sutmann, J. Grotendorst, G. Gompper, D. Marx (Eds.), pages 575-598,   (full paper pdf),   2015
o 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.),   (full paper pdf),   2014
o Heider, S., Kunis, S., Potts, D., Veit, M. A sparse Prony FFT. Proceedings of the 10th International Conference on Sampling Theory and Applications, pages 572-575   (full paper pdf),   2013
o Nestler, F., Potts, D. Fast Ewald summation under 2d- and 1d-periodic boundary conditions based on NFFTs. Proceedings of the 10th International Conference on Sampling Theory and Applications, pages 568-571   (full paper pdf),   2013
o Gräf, M., Potts, D., Steidl, G. Quadrature nodes meet stippling dots. in Lecture Notes in Computer Science 6667   (full paper pdf),   2011
o Pippig, M., Potts, D. Particle simulation based on nonequispaced fast Fourier transforms. in: Fast Methods for Long-Range Interactions in Complex Systems, G. Sutmann, P. Gibbon, T. Lippert (Eds.), pages 131-158.   (full paper pdf),   2010
o Keiner, J., Kunis, S., Potts, D. Efficient reconstruction of functions on the sphere from scattered data. in: PAMM, Proc. Appl. Math. Mech. 7, pages 1050405-1050406.   (full paper ps, pdf),   2007
o Schaeben, H., Hielscher, R., Fundenberger, J.-J., Potts, D., Prestin, J. Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids. in: Proceedings IAMG'2007, Zhao, P., Agterberg, F., Chen, Q., (Eds.), Beijing, pages 48-50. (full paper ps, pdf ),   2007
o Eggers, H., Knopp, T. , Potts, D. Fast Fourier transform for nonequispaced data with applications in MRI. in: Jahrestagung der Deutschen Sektion der ISMRM.   (full paper ps, pdf),   2006
o Kunis, S., Knopp, T. , Potts, D. Inverse nonequispaced FFT - Applications in MRI and numerical stability. in: Jahrestagung der Deutschen Sektion der ISMRM.   (full paper ps, pdf),   2006
o Pöplau, G., Potts, D., van Rienen, U. Calculation of 3D Space-Charge Fields of Bunches of Charged Particles by Fast Summation. in: Scientific Computing in Electrical Engineering, A.M. Anile, G. Ali and G. Mascaly (Eds.), Springer-Verlag, Berlin, pages 241-246. (full paper ps, pdf ),   2006
o Heldmann, S., Mahnke, O., Potts, D., Modersitzki, J. and Fischer, B. Fast computation of Mutual Information in a variational image registration approach. in: Proceedings of the BVM 2004, "Bildverarbeitung für die Medizin 2004, Algorithmen - Systeme - Anwendungen" 29. - 30. März 2004, Berlin. (full paper pdf),   2004
o Pöplau,G., Potts, D. Fast Poisson solvers on nonequispaced grids: Multigrid and Fourier methods compared. in: Proceedings of SPIE: Advanced Signal Processing Algorithms, Architectures and Implementations XIII, F.T. Luk (Ed.), Vol. 5205. (full paper ps, pdf),   2003
o Böhme, M., Potts, D. A Fast Alogorithm for Spherical Filtering on Arbitrary Grids. in: Proceedings of SPIE: Wavelets Applications in Signal and Image Processing X, M.A. Unser, A. Aldroubi, A.F. Laine (Eds.), Vol. 5207. (full paper ps, pdf) ,   2003
o Potts, D., Steidl, G. Preconditioning of Hermitian block-Toeplitz-Toeplitz-block matrices by level-1 preconditioners. in: Structured Matrices in Mathematics, Computer Science, and Engineering II, V. Olshevsky, (Ed.), pages 193-212. (full paper ps, pdf),   2001
o Schaeben, H., Potts, D., Prestin, J. Spherical Wavelets with an application in preferred crystallographic orientation. in: Proceedings of the Annual Conference of the International Association for Mathematical Geology, Cancun, Mexico. (full paper ps.Z, pdf),   2001
o Schaeben, H., Prestin, J., Potts, D. Wavelet representation of diffraction pole figures. in: Advances in X-ray Analysis 44, Proceedings of the 49th Denver X-ray Conference, Denver 2000, pages 235-240. (full paper ps, pdf),   2000
o Potts, D., Steidl, G. New Fourier reconstruction algorithms for computerized tomography. in: Proceedings of SPIE: Wavelet Applications in Signal and Image Processing VIII,A. Aldroubi,A.F. Laine,M.A. Unser (Eds.), Vol.:4119, pages 13-23. (full paper ps, pdf),   2000
o Potts, D., Steidl, G., and Tasche M. Fast Fourier transforms for nonequispaced data: A tutorial. in: Modern Sampling Theory: Mathematics and Applications, J.J. Benedetto, P. Ferreira (Eds.), Chapter 12, pages 249-274. (full paper ps.Z, pdf),   1998
o Potts, D., Steidl, G., Tasche, M. Trigonometric preconditioners for block Toeplitz systems. in: Multivariate Approximation and Splines, (Eds. G. Nürnberger, J.W. Schmidt, and G. Walz) Birkhäuser, Basel 1997, pages 219-234. (full paper ps.Z, pdf),   1997
o Potts, D., Steidl, G., Tasche, M. Kernels of spherical harmonics and spherical frames. in: Fontanella, F, Jetter, K. & Laurent, P.J. (eds.), Advanced Topics in Multivariate Approximation, World Scientific Publ., Singapore, pages 287-301. (full paper ps.gz, pdf),   1996
o Potts, D., Tasche, M. Interpolatory wavelets on the sphere. in: Chui, C.K., Schumaker, L.L. (Eds.), Approximation Theory VIII, Vol. 2: Wavelets and Multilevel Approximation, World Scientific Publ., Singapore: pages 335-342. (full paper ps.gz, pdf),   1995