Dick, Josef; Goda, Takashi; Suzuki, Kosuke Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate. (English) Zbl 1504.11085 Math. Comput. 91, No. 338, 2771-2801 (2022). Reviewer: Symon Serbenyuk (Kyïv) MSC: 11K45 65C05 65D30 65D32 PDFBibTeX XMLCite \textit{J. Dick} et al., Math. Comput. 91, No. 338, 2771--2801 (2022; Zbl 1504.11085) Full Text: DOI arXiv
Dick, Josef; Feischl, Michael A quasi-Monte Carlo data compression algorithm for machine learning. (English) Zbl 07418854 J. Complexity 67, Article ID 101587, 25 p. (2021). MSC: 65C05 65D30 65D32 PDFBibTeX XMLCite \textit{J. Dick} and \textit{M. Feischl}, J. Complexity 67, Article ID 101587, 25 p. (2021; Zbl 07418854) Full Text: DOI arXiv
Dick, Josef; Goda, Takashi Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. (English) Zbl 1484.65005 J. Comput. Appl. Math. 382, Article ID 113062, 15 p. (2021). MSC: 65C05 41A55 41A63 65D30 65D32 11K38 PDFBibTeX XMLCite \textit{J. Dick} and \textit{T. Goda}, J. Comput. Appl. Math. 382, Article ID 113062, 15 p. (2021; Zbl 1484.65005) Full Text: DOI arXiv
Dick, Josef; Goda, Takashi; Yoshiki, Takehito Richardson extrapolation of polynomial lattice rules. (English) Zbl 1415.65058 SIAM J. Numer. Anal. 57, No. 1, 44-69 (2019). Reviewer: Dan Bărbosu (Baia Mare) MSC: 65D32 65C05 65D30 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM J. Numer. Anal. 57, No. 1, 44--69 (2019; Zbl 1415.65058) Full Text: DOI arXiv
Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito Digital net properties of a polynomial analogue of Frolov’s construction. (English) Zbl 1421.11060 Finite Fields Appl. 51, 325-350 (2018). MSC: 11K31 11K38 11P21 65D32 PDFBibTeX XMLCite \textit{J. Dick} et al., Finite Fields Appl. 51, 325--350 (2018; Zbl 1421.11060) Full Text: DOI arXiv
Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich On the optimal order of integration in Hermite spaces with finite smoothness. (English) Zbl 06862953 SIAM J. Numer. Anal. 56, No. 2, 684-707 (2018). MSC: 65D30 65D32 65Y20 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM J. Numer. Anal. 56, No. 2, 684--707 (2018; Zbl 06862953) Full Text: DOI arXiv
Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. (English) Zbl 1385.65003 Ann. Mat. Pura Appl. (4) 197, No. 1, 109-126 (2018). Reviewer: Rózsa Horváth-Bokor (Budakalász) MSC: 65C05 65D32 11K31 PDFBibTeX XMLCite \textit{J. Dick} et al., Ann. Mat. Pura Appl. (4) 197, No. 1, 109--126 (2018; Zbl 1385.65003) Full Text: DOI arXiv
Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito Construction of interlaced polynomial lattice rules for infinitely differentiable functions. (English) Zbl 1385.65002 Numer. Math. 137, No. 2, 257-288 (2017). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 65D32 65C10 65C20 65T50 PDFBibTeX XMLCite \textit{J. Dick} et al., Numer. Math. 137, No. 2, 257--288 (2017; Zbl 1385.65002) Full Text: DOI arXiv
Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. (English) Zbl 1398.65031 SIAM/ASA J. Uncertain. Quantif. 4, 48-79 (2016). MSC: 65D30 65D32 65N30 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM/ASA J. Uncertain. Quantif. 4, 48--79 (2016; Zbl 1398.65031) Full Text: DOI arXiv
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich Numerical integration in log-Korobov and log-cosine spaces. (English) Zbl 1339.65008 Numer. Algorithms 70, No. 4, 753-775 (2015). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 65D32 PDFBibTeX XMLCite \textit{J. Dick} et al., Numer. Algorithms 70, No. 4, 753--775 (2015; Zbl 1339.65008) Full Text: DOI arXiv
Goda, Takashi; Dick, Josef Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. (English) Zbl 1323.65002 Found. Comput. Math. 15, No. 5, 1245-1278 (2015). MSC: 65C05 65D30 65D32 PDFBibTeX XMLCite \textit{T. Goda} and \textit{J. Dick}, Found. Comput. Math. 15, No. 5, 1245--1278 (2015; Zbl 1323.65002) Full Text: DOI arXiv
Brauchart, J. S.; Dick, J.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. (English) Zbl 1325.65037 J. Math. Anal. Appl. 431, No. 2, 782-811 (2015). MSC: 65D30 41A63 41A55 65D32 PDFBibTeX XMLCite \textit{J. S. Brauchart} et al., J. Math. Anal. Appl. 431, No. 2, 782--811 (2015; Zbl 1325.65037) Full Text: DOI arXiv
Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. (English) Zbl 1326.65013 SIAM J. Numer. Anal. 52, No. 6, 2676-2702 (2014). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 65D30 65D32 65N30 65N75 35R60 45R05 65C30 60H25 60G60 65J10 PDFBibTeX XMLCite \textit{J. Dick} et al., SIAM J. Numer. Anal. 52, No. 6, 2676--2702 (2014; Zbl 1326.65013) Full Text: DOI arXiv Link
Dick, Josef; Gnewuch, Michael Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. (English) Zbl 1296.41025 J. Approx. Theory 184, 111-145 (2014). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A55 28A25 65C05 65D32 65Y20 68W40 PDFBibTeX XMLCite \textit{J. Dick} and \textit{M. Gnewuch}, J. Approx. Theory 184, 111--145 (2014; Zbl 1296.41025) Full Text: DOI arXiv
Dick, Josef Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. (English) Zbl 1291.65013 J. Approx. Theory 183, 14-30 (2014). MSC: 65C05 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{J. Dick}, J. Approx. Theory 183, 14--30 (2014; Zbl 1291.65013) Full Text: DOI arXiv
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich Lattice rules for nonperiodic smooth integrands. (English) Zbl 1345.65070 Numer. Math. 126, No. 2, 259-291 (2014). MSC: 65T40 42A16 46E22 65D32 PDFBibTeX XMLCite \textit{J. Dick} et al., Numer. Math. 126, No. 2, 259--291 (2014; Zbl 1345.65070) Full Text: DOI arXiv Link
Dick, Josef (ed.); Kuo, Frances Y. (ed.); Peters, Gareth W. (ed.); Sloan, Ian H. (ed.) 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. (English) Zbl 1282.65007 Springer Proceedings in Mathematics & Statistics 65. Berlin: Springer (ISBN 978-3-642-41094-9/hbk; 978-3-642-41095-6/ebook). xii, 686 p. (2013). MSC: 65-06 65C05 65C10 65D30 65D32 11K45 00B25 PDFBibTeX XMLCite \textit{J. Dick} (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 (2013; Zbl 1282.65007) Full Text: DOI arXiv
Dick, Josef Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm. (English) Zbl 1264.65030 Numer. Math. 122, No. 3, 443-467 (2012). Reviewer: Alexandru Mihai Bica (Oradea) MSC: 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{J. Dick}, Numer. Math. 122, No. 3, 443--467 (2012; Zbl 1264.65030) Full Text: DOI arXiv
Brauchart, Johann S.; Dick, Josef Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). (English) Zbl 1258.65003 Numer. Math. 121, No. 3, 473-502 (2012). Reviewer: Vassil Grozdanov (Blagoevgrad) MSC: 65C05 11K06 11K36 11K38 65D32 41A55 41A63 11K45 46E22 PDFBibTeX XMLCite \textit{J. S. Brauchart} and \textit{J. Dick}, Numer. Math. 121, No. 3, 473--502 (2012; Zbl 1258.65003) Full Text: DOI arXiv
Dick, Josef A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules. arXiv:1207.5275 Preprint, arXiv:1207.5275 [math.NA] (2012). MSC: 65D30 65D32 BibTeX Cite \textit{J. Dick}, ``A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules'', Preprint, arXiv:1207.5275 [math.NA] (2012) Full Text: arXiv OA License
Dick, Josef; Pillichshammer, Friedrich Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. (English) Zbl 1282.65012 Cambridge: Cambridge University Press (ISBN 978-0-521-19159-3/hbk). xvii, 600 p. (2010). Reviewer: József Sándor (Cluj-Napoca) MSC: 65C05 65-02 11K06 11K38 11K45 46E35 65D32 PDFBibTeX XMLCite \textit{J. Dick} and \textit{F. Pillichshammer}, Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Cambridge: Cambridge University Press (2010; Zbl 1282.65012)
Baldeaux, Jan; Dick, Josef QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. (English) Zbl 1186.65005 Constr. Approx. 30, No. 3, 495-527 (2009). Reviewer: Serghey G. Suvorov (Donetsk) MSC: 65C05 11K38 11K45 46E22 65D32 PDFBibTeX XMLCite \textit{J. Baldeaux} and \textit{J. Dick}, Constr. Approx. 30, No. 3, 495--527 (2009; Zbl 1186.65005) Full Text: DOI
Dick, Josef Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. (English) Zbl 1158.65007 SIAM J. Numer. Anal. 45, No. 5, 2141-2176 (2007). Reviewer: Christian Lecot (Le Bourget-du-Lac) MSC: 65C05 11K45 42C10 11K38 65D32 46E22 PDFBibTeX XMLCite \textit{J. Dick}, SIAM J. Numer. Anal. 45, No. 5, 2141--2176 (2007; Zbl 1158.65007) Full Text: DOI arXiv
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. On the existence of higher order polynomial lattices based on a generalized figure of merit. (English) Zbl 1130.65047 J. Complexity 23, No. 4-6, 581-593 (2007). Reviewer: Volker Ziegler (Graz) MSC: 65D30 65D32 11K36 PDFBibTeX XMLCite \textit{J. Dick} et al., J. Complexity 23, No. 4--6, 581--593 (2007; Zbl 1130.65047) Full Text: DOI
Dick, Josef; Pillichshammer, Friedrich Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. (English) Zbl 1130.65005 J. Complexity 23, No. 4-6, 436-453 (2007). Reviewer: Manfred Tasche (Rostock) MSC: 65C05 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{J. Dick} and \textit{F. Pillichshammer}, J. Complexity 23, No. 4--6, 436--453 (2007; Zbl 1130.65005) Full Text: DOI
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H. Construction algorithms for polynomial lattice rules for multivariate integration. (English) Zbl 1079.65007 Math. Comput. 74, No. 252, 1895-1921 (2005). Reviewer: R. E. Maiboroda (Kyïv) MSC: 65C05 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{J. Dick} et al., Math. Comput. 74, No. 252, 1895--1921 (2005; Zbl 1079.65007) Full Text: DOI
Wang, Xiaoqun; Sloan, Ian H.; Dick, Josef On Korobov lattice rules in weighted spaces. (English) Zbl 1079.65010 SIAM J. Numer. Anal. 42, No. 4, 1760-1779 (2004). Reviewer: R. E. Maiboroda (Kyïv) MSC: 65C05 65D32 PDFBibTeX XMLCite \textit{X. Wang} et al., SIAM J. Numer. Anal. 42, No. 4, 1760--1779 (2004; Zbl 1079.65010) Full Text: DOI