Gross, Craig; Iwen, Mark; Kämmerer, Lutz; Volkmer, Toni Sparse Fourier transforms on rank-1 lattices for the rapid and low-memory approximation of functions of many variables. (English) Zbl 1478.65143 Sampl. Theory Signal Process. Data Anal. 20, No. 1, Paper No. 1, 45 p. (2022). MSC: 65T40 65D15 42B05 65Y20 65T50 PDFBibTeX XMLCite \textit{C. Gross} et al., Sampl. Theory Signal Process. Data Anal. 20, No. 1, Paper No. 1, 45 p. (2022; Zbl 1478.65143) Full Text: DOI arXiv
Gross, Craig; Iwen, Mark A.; Kämmerer, Lutz; Volkmer, Toni A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size. (English) Zbl 1481.65275 Adv. Comput. Math. 47, No. 6, Paper No. 86, 24 p. (2021). MSC: 65T40 65T50 42B05 42B35 68Q25 PDFBibTeX XMLCite \textit{C. Gross} et al., Adv. Comput. Math. 47, No. 6, Paper No. 86, 24 p. (2021; Zbl 1481.65275) Full Text: DOI arXiv
Kämmerer, Lutz; Potts, Daniel; Volkmer, Toni High-dimensional sparse FFT based on sampling along multiple rank-1 lattices. (English) Zbl 1467.65120 Appl. Comput. Harmon. Anal. 51, 225-257 (2021). MSC: 65T40 42A10 PDFBibTeX XMLCite \textit{L. Kämmerer} et al., Appl. Comput. Harmon. Anal. 51, 225--257 (2021; Zbl 1467.65120) Full Text: DOI arXiv
Kämmerer, Lutz; Volkmer, Toni Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices. (English) Zbl 1455.65240 J. Approx. Theory 246, 1-27 (2019). MSC: 65T40 42B05 42B35 65D30 65T50 65Y20 PDFBibTeX XMLCite \textit{L. Kämmerer} and \textit{T. Volkmer}, J. Approx. Theory 246, 1--27 (2019; Zbl 1455.65240) Full Text: DOI arXiv
Kämmerer, Lutz Multiple rank-1 lattices as sampling schemes for multivariate trigonometric polynomials. (English) Zbl 1401.65155 J. Fourier Anal. Appl. 24, No. 1, 17-44 (2018). Reviewer: Xiaosheng Zhuang (Hong Kong) MSC: 65T40 65T50 PDFBibTeX XMLCite \textit{L. Kämmerer}, J. Fourier Anal. Appl. 24, No. 1, 17--44 (2018; Zbl 1401.65155) Full Text: DOI
Byrenheid, Glenn; Kämmerer, Lutz; Ullrich, Tino; Volkmer, Toni Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness. (English) Zbl 1422.65467 Numer. Math. 136, No. 4, 993-1034 (2017). Reviewer: Jiří Hrivnák (Praha) MSC: 65T40 42A10 65D30 65D32 68Q17 68Q25 42B35 65T50 65Y20 PDFBibTeX XMLCite \textit{G. Byrenheid} et al., Numer. Math. 136, No. 4, 993--1034 (2017; Zbl 1422.65467) Full Text: DOI arXiv
Kämmerer, Lutz; Potts, Daniel; Volkmer, Toni Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling. (English) Zbl 1320.65204 J. Complexity 31, No. 4, 543-576 (2015). MSC: 65T40 42C40 65T50 PDFBibTeX XMLCite \textit{L. Kämmerer} et al., J. Complexity 31, No. 4, 543--576 (2015; Zbl 1320.65204) Full Text: DOI
Kämmerer, Lutz; Potts, Daniel; Volkmer, Toni Approximation of multivariate periodic functions by trigonometric polynomials based on sampling along rank-1 lattice with generating vector of Korobov form. (English) Zbl 1318.42006 J. Complexity 31, No. 3, 424-456 (2015). MSC: 42B05 42A10 42A05 65T40 65T50 PDFBibTeX XMLCite \textit{L. Kämmerer} et al., J. Complexity 31, No. 3, 424--456 (2015; Zbl 1318.42006) Full Text: DOI
Kämmerer, Lutz Reconstructing multivariate trigonometric polynomials from samples along rank-1 lattices. (English) Zbl 1325.65189 Fasshauer, Gregory E. (ed.) et al., Approximation theory XIV: San Antonio 2013. Selected papers based on the presentations at the international conference, San Antonio, TX, USA, April 7–10, 2013. Cham: Springer (ISBN 978-3-319-06403-1/hbk; 978-3-319-06404-8/ebook). Springer Proceedings in Mathematics & Statistics 83, 255-271 (2014). MSC: 65T40 65T50 PDFBibTeX XMLCite \textit{L. Kämmerer}, Springer Proc. Math. Stat. 83, 255--271 (2014; Zbl 1325.65189) Full Text: DOI
Kämmerer, Lutz Reconstructing multivariate trigonometric polynomials by sampling along generated sets. (English) Zbl 1302.65288 Dick, Josef (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of the 10th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Sydney, Australia, February 13–17, 2012. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). Springer Proceedings in Mathematics & Statistics 65, 439-454 (2013). MSC: 65T40 42B05 65T50 PDFBibTeX XMLCite \textit{L. Kämmerer}, Springer Proc. Math. Stat. 65, 439--454 (2013; Zbl 1302.65288) Full Text: DOI
Kämmerer, Lutz; Kunis, Stefan; Potts, Daniel Interpolation lattices for hyperbolic cross trigonometric polynomials. (English) Zbl 1335.65105 J. Complexity 28, No. 1, 76-92 (2012). Reviewer: Roza Aceska (Muncie) MSC: 65T40 42A15 65T50 65D32 PDFBibTeX XMLCite \textit{L. Kämmerer} et al., J. Complexity 28, No. 1, 76--92 (2012; Zbl 1335.65105) Full Text: DOI