Edit Profile (opens in new tab) Dick, Josef Co-Author Distance Author ID: dick.josef Published as: Dick, Josef; Dick, J. Homepage: https://web.maths.unsw.edu.au/~josefdick/ External Links: MGP · ORCID · Google Scholar Documents Indexed: 125 Publications since 2004, including 2 Books and 8 Additional arXiv Preprints 3 Contributions as Editor Co-Authors: 60 Co-Authors with 112 Joint Publications 1,512 Co-Co-Authors all top 5 Co-Authors 16 single-authored 46 Pillichshammer, Friedrich 15 Kritzer, Peter 11 Kuo, Frances Y. 9 Schwab, Christoph 8 Baldeaux, Jan 8 Le Gia, Quoc Thong 8 Leobacher, Gunther 8 Sloan, Ian Hugh 6 Brauchart, Johann S. 6 Goda, Takashi 6 Zhu, Houying 5 Hinrichs, Aicke 5 Woźniakowski, Henryk 4 Suzuki, Kosuke 4 Yoshiki, Takehito 3 Aistleitner, Christoph 3 Feischl, Michael 3 Mustapha, Kassem 3 Niederreiter, Harald 3 Nuyens, Dirk 3 Rudolf, Daniel 3 Wang, Xiaoqun 2 Chen, Su 2 Gantner, Robert Nicholas 2 Gnewuch, Michael 2 Hickernell, Fred J. 2 Longo, Marcello 2 Markhasin, Lev 2 McLean, William 2 Owen, Art B. 2 Ullrich, Mario 2 Waterhouse, Benjamin J. 1 An, Xin 1 Bilyk, Dmitry 1 Cui, Tiangang 1 Ebert, Adrian 1 Ehler, Martin 1 Fang, Lou 1 Gomez-Perez, Domingo 1 Gräf, Manuel 1 Greslehner, Julia 1 Gunawan, David 1 Herrmann, Lukas 1 Irrgeher, Christian 1 Kohn, Robert J. 1 Krattenthaler, Christian Friedrich 1 Larchner, Gerhard 1 LeGia, T. 1 Liu, Kwong-Ip 1 Matsumoto, Makoto 1 Murata, Hiroya 1 Peters, Gareth William 1 Pirsic, Isabel 1 Prochno, Joscha 1 Saff, Edward Barry 1 Scaglioni, Andrea 1 Schmid, Wolfgang Ch. 1 Tran, Minh Ngoc 1 Wang, Yuguang 1 Winterhof, Arne all top 5 Serials 17 Journal of Complexity 11 SIAM Journal on Numerical Analysis 8 Mathematics of Computation 7 Numerische Mathematik 4 Acta Arithmetica 4 Journal of Computational and Applied Mathematics 3 Proceedings of the American Mathematical Society 3 Constructive Approximation 3 Finite Fields and their Applications 3 Statistics and Computing 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Statistics 2 Archiv der Mathematik 2 Journal of Approximation Theory 2 Numerical Algorithms 2 Monte Carlo Methods and Applications 2 Foundations of Computational Mathematics 2 SIAM/ASA Journal on Uncertainty Quantification 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Discrete Mathematics 1 IMA Journal of Numerical Analysis 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Computing 1 Journal of Number Theory 1 Mathematics and Computers in Simulation 1 Mathematika 1 Monatshefte für Mathematik 1 Statistics & Probability Letters 1 Acta Mathematica Hungarica 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 The Annals of Applied Probability 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Scientific Computing 1 Electronic Journal of Probability 1 Integers 1 Acta Numerica 1 International Journal of Numerical Analysis and Modeling 1 Springer Series in Computational Mathematics 1 Uniform Distribution Theory 1 Electronic Journal of Statistics 1 Radon Series on Computational and Applied Mathematics 1 Information and Inference 1 Springer Proceedings in Mathematics & Statistics all top 5 Fields 97 Numerical analysis (65-XX) 71 Number theory (11-XX) 16 Approximations and expansions (41-XX) 13 Probability theory and stochastic processes (60-XX) 12 Statistics (62-XX) 9 Functional analysis (46-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 5 Partial differential equations (35-XX) 3 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 115 Publications have been cited 1,960 times in 808 Documents Cited by ▼ Year ▼ Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012 Dick, Josef; Pillichshammer, Friedrich 341 2010 High-dimensional integration: The quasi-Monte Carlo way. Zbl 1296.65004 Dick, Josef; Kuo, Frances Y.; Sloan, Ian H. 233 2013 Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. Zbl 1189.42012 Dick, Josef 75 2008 Good lattice rules in weighted Korobov spaces with general weights. Zbl 1097.65004 Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk 62 2006 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 58 2014 Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021 Dick, Josef; Pillichshammer, Friedrich 50 2005 Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Zbl 1158.65007 Dick, Josef 44 2007 On the convergence rate of the component-by-component construction of good lattice rules. Zbl 1344.65034 Dick, Josef 42 2004 Liberating the weights. Zbl 1089.65005 Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk 41 2004 Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007 Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H. 39 2005 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 38 2014 Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077 Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk 36 2011 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 31 2017 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070 Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 31 2014 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 28 2016 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031 Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 25 2016 Optimal \(\mathcal {L}_{2}\) discrepancy bounds for higher order digital sequences over the finite field \(\mathbb {F}_{2}\). Zbl 1294.11127 Dick, Josef; Pillichshammer, Friedrich 24 2014 A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024 Brauchart, Johann S.; Dick, Josef 24 2013 Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038 Aistleitner, Christoph; Dick, Josef 23 2015 Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005 Dick, Josef; Pillichshammer, Friedrich 22 2007 Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002 Goda, Takashi; Dick, Josef 22 2015 Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Zbl 1244.65002 Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich 22 2012 The construction of good extensible rank-1 lattices. Zbl 1211.11092 Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. 21 2008 Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003 Aistleitner, C.; Brauchart, J. S.; Dick, J. 21 2012 The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027 Dick, Josef 20 2009 On the mean square weighted \({\mathcal L}_2\) discrepancy of randomized digital \((t,m,s)\)-nets over \({\mathbb Z}_2\). Zbl 1080.11058 Dick, Josef; Pillichshammer, Friedrich 19 2005 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086 Dick, Josef; Pillichshammer, Friedrich 19 2014 QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005 Baldeaux, Jan; Dick, Josef 18 2009 Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040 Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 16 2005 Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011 Dick, Josef 15 2011 On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004 Dick, Josef 15 2009 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061 Dick, Josef; Pillichshammer, Friedrich 14 2014 Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. Zbl 1325.65037 Brauchart, J. S.; Dick, J.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 14 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 14 2015 Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 13 2019 Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003 Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich 13 2011 A characterization of Sobolev spaces on the sphere and an extension of Stolarsky’s invariance principle to arbitrary smoothness. Zbl 1284.41013 Brauchart, Johann S.; Dick, Josef 13 2013 Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. Zbl 1296.41025 Dick, Josef; Gnewuch, Michael 13 2014 Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. Zbl 1312.65002 Dick, Josef; Gnewuch, Michael 12 2014 Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010 Chen, S.; Dick, J.; Owen, A. B. 12 2011 Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\). Zbl 1286.11120 Dick, Josef 12 2014 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078 Dick, Josef; Pillichshammer, Friedrich 11 2015 Duality theory and propagation rules for generalized digital nets. Zbl 1219.11115 Dick, Josef; Kritzer, Peter 11 2010 On Korobov lattice rules in weighted spaces. Zbl 1079.65010 Wang, Xiaoqun; Sloan, Ian H.; Dick, Josef 10 2004 Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003 Brauchart, Johann S.; Dick, Josef 10 2012 On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953 Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich 9 2018 Lattice-Nyström method for Fredholm integral equations of the second kind with convolution type kernels. Zbl 1131.65108 Dick, Josef; Kritzer, Peter; Kuo, Frances Y.; Sloan, Ian H. 9 2007 Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023 Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich 9 2006 Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. Zbl 1484.65005 Dick, Josef; Goda, Takashi 9 2021 Lattice rules. Numerical integration, approximation, and discrepancy. Zbl 07566616 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich 9 2022 A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004 Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 9 2015 On the fast computation of the weight enumerator polynomial and the \(t\) value of digital nets over finite abelian groups. Zbl 1316.11068 Dick, Josef; Matsumoto, Makoto 9 2013 Equidistribution properties of generalized nets and sequences. Zbl 1228.65007 Dick, Josef; Baldeaux, Jan 9 2009 On the exact \(t\)-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031 Dick, Josef; Niederreiter, Harald 8 2008 A note on the existence of sequences with small star discrepancy. Zbl 1132.11041 Dick, Josef 8 2007 Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010 8 2018 Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079 Aistleitner, Christoph; Dick, Josef 8 2014 The construction of extensible polynomial lattice rules with small weighted star discrepancy. Zbl 1135.11039 Dick, Josef 7 2007 On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 7 2007 Reducing the construction cost of the component-by-component construction of good lattice rules. Zbl 1051.65003 Dick, J.; Kuo, F. Y. 7 2004 Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003 Dick, Josef; Pillichshammer, Friedrich 7 2005 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060 Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 7 2017 Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013 Dick, Josef 7 2014 Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113 Zhu, Houying; Dick, Josef 7 2014 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002 Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 6 2007 Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins. Zbl 1430.62101 Gunawan, D.; Tran, M.-N.; Suzuki, K.; Dick, J.; Kohn, R. 6 2019 Higher order Sobol’ indices. Zbl 1309.62098 Owen, Art B.; Dick, Josef; Chen, Su 6 2014 Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005 Brauchart, Johann S.; Dick, Josef; Fang, Lou 6 2015 Duality theory and propagation rules for higher order nets. Zbl 1229.11103 Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 6 2011 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025 Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 5 2006 A Taylor space for multivariate integration. Zbl 1103.65007 Dick, Josef 5 2006 A best possible upper bound on the star discrepancy of \((t,m,2)\)-nets. Zbl 1103.11022 Dick, Josef; Kritzer, Peter 5 2006 Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. Zbl 1351.60100 Dick, Josef; Rudolf, Daniel; Zhu, Houying 5 2016 Fast QMC matrix-vector multiplication. Zbl 1320.65008 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 5 2015 Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058 Dick, Josef; Goda, Takashi; Yoshiki, Takehito 5 2019 On a projection-corrected component-by-component construction. Zbl 1329.65007 Dick, Josef; Kritzer, Peter 5 2016 Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359 Dick, Josef; Feischl, Michael; Schwab, Christoph 5 2019 Constructing good lattice rules with millions of points. Zbl 1043.65002 Dick, Josef; Kuo, Frances Y. 4 2004 Approximation of functions using digital nets. Zbl 1153.65314 Dick, Josef; Kritzer, Peter; Kuo, Frances Y. 4 2008 Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095 Dick, Josef 4 2008 Star discrepancy estimates for digital \((t,m,2)\)-nets and digital \((t,2)\)-sequences over \(\mathbb Z_2\). Zbl 1102.11036 Dick, J.; Kritzer, P. 4 2005 Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Zbl 1385.65002 Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito 4 2017 A note on the periodic \(L_2\)-discrepancy of Korobov’s \(p\)-sets. Zbl 1448.11148 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 4 2020 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044 Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 4 2017 Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136 Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 4 2017 On the mean square weighted \(\mathcal {L}_2\) discrepancy of randomized digital nets in prime base. Zbl 1142.11345 Cristea, Ligia L.; Dick, Josef; Pillichshammer, Friedrich 3 2006 Periodic functions with bounded remainder. Zbl 1115.11044 Dick, Josef; Pillichshammer, Friedrich 3 2006 The construction of good extensible Korobov rules. Zbl 1131.11051 Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 3 2007 Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039 Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 3 2007 Dyadic diaphony of digital nets over \(\mathbb Z_2\). Zbl 1130.11042 Dick, Josef; Pillichshammer, Friedrich 3 2005 Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate. Zbl 1504.11085 Dick, Josef; Goda, Takashi; Suzuki, Kosuke 3 2022 A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010 Baldeaux, Jan; Dick, Josef 3 2011 A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071 Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 3 2010 Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm. Zbl 1264.65030 Dick, Josef 3 2012 A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005 Dick, Josef; Rudolf, Daniel; Zhu, Houying 3 2019 A quasi-Monte Carlo data compression algorithm for machine learning. Zbl 07418854 Dick, Josef; Feischl, Michael 2 2021 Tractability properties of the discrepancy in Orlicz norms. Zbl 1470.46050 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich; Prochno, Joscha 2 2020 Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. Zbl 1385.65003 Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito 2 2018 Applications of geometric discrepancy in numerical analysis and statistics. Zbl 1368.11077 Dick, Josef 2 2014 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048 Dick, Josef; Pillichshammer, Friedrich 2 2014 Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold. Zbl 07698576 Dick, Josef; Ehler, Martin; Gräf, Manuel; Krattenthaler, Christian 1 2023 Lattice rules. Numerical integration, approximation, and discrepancy. Zbl 07566616 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich 9 2022 Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate. Zbl 1504.11085 Dick, Josef; Goda, Takashi; Suzuki, Kosuke 3 2022 Extrapolated polynomial lattice rule integration in computational uncertainty quantification. Zbl 1494.65004 Dick, Josef; Longo, Marcello; Schwab, Christoph 1 2022 Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. Zbl 1484.65005 Dick, Josef; Goda, Takashi 9 2021 A quasi-Monte Carlo data compression algorithm for machine learning. Zbl 07418854 Dick, Josef; Feischl, Michael 2 2021 Weighted integration over a hyperrectangle based on digital nets and sequences. Zbl 1467.65019 Dick, Josef; Pillichshammer, Friedrich 1 2021 A note on the periodic \(L_2\)-discrepancy of Korobov’s \(p\)-sets. Zbl 1448.11148 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 4 2020 Tractability properties of the discrepancy in Orlicz norms. Zbl 1470.46050 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich; Prochno, Joscha 2 2020 Discrepancy theory. Zbl 1454.11006 1 2020 Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 13 2019 Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins. Zbl 1430.62101 Gunawan, D.; Tran, M.-N.; Suzuki, K.; Dick, J.; Kohn, R. 6 2019 Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058 Dick, Josef; Goda, Takashi; Yoshiki, Takehito 5 2019 Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359 Dick, Josef; Feischl, Michael; Schwab, Christoph 5 2019 A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005 Dick, Josef; Rudolf, Daniel; Zhu, Houying 3 2019 On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953 Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich 9 2018 Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010 8 2018 Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. Zbl 1385.65003 Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito 2 2018 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 31 2017 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060 Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 7 2017 Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Zbl 1385.65002 Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito 4 2017 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044 Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 4 2017 Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136 Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 4 2017 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 28 2016 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031 Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 25 2016 Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. Zbl 1351.60100 Dick, Josef; Rudolf, Daniel; Zhu, Houying 5 2016 On a projection-corrected component-by-component construction. Zbl 1329.65007 Dick, Josef; Kritzer, Peter 5 2016 Discrepancy estimates for acceptance-rejection samplers using stratified inputs. Zbl 1356.65014 Zhu, Houying; Dick, Josef 1 2016 Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038 Aistleitner, Christoph; Dick, Josef 23 2015 Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002 Goda, Takashi; Dick, Josef 22 2015 Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. Zbl 1325.65037 Brauchart, J. S.; Dick, J.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 14 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002 Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 14 2015 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078 Dick, Josef; Pillichshammer, Friedrich 11 2015 A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004 Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 9 2015 Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005 Brauchart, Johann S.; Dick, Josef; Fang, Lou 6 2015 Fast QMC matrix-vector multiplication. Zbl 1320.65008 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 5 2015 Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008 Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 1 2015 Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017 Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph 1 2015 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 58 2014 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 38 2014 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070 Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 31 2014 Optimal \(\mathcal {L}_{2}\) discrepancy bounds for higher order digital sequences over the finite field \(\mathbb {F}_{2}\). Zbl 1294.11127 Dick, Josef; Pillichshammer, Friedrich 24 2014 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086 Dick, Josef; Pillichshammer, Friedrich 19 2014 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061 Dick, Josef; Pillichshammer, Friedrich 14 2014 Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. Zbl 1296.41025 Dick, Josef; Gnewuch, Michael 13 2014 Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. Zbl 1312.65002 Dick, Josef; Gnewuch, Michael 12 2014 Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\). Zbl 1286.11120 Dick, Josef 12 2014 Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079 Aistleitner, Christoph; Dick, Josef 8 2014 Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013 Dick, Josef 7 2014 Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113 Zhu, Houying; Dick, Josef 7 2014 Higher order Sobol’ indices. Zbl 1309.62098 Owen, Art B.; Dick, Josef; Chen, Su 6 2014 Applications of geometric discrepancy in numerical analysis and statistics. Zbl 1368.11077 Dick, Josef 2 2014 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048 Dick, Josef; Pillichshammer, Friedrich 2 2014 Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo. Zbl 1309.65004 Dick, Josef; Rudolf, Daniel 2 2014 High-dimensional integration: The quasi-Monte Carlo way. Zbl 1296.65004 Dick, Josef; Kuo, Frances Y.; Sloan, Ian H. 233 2013 A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024 Brauchart, Johann S.; Dick, Josef 24 2013 A characterization of Sobolev spaces on the sphere and an extension of Stolarsky’s invariance principle to arbitrary smoothness. Zbl 1284.41013 Brauchart, Johann S.; Dick, Josef 13 2013 On the fast computation of the weight enumerator polynomial and the \(t\) value of digital nets over finite abelian groups. Zbl 1316.11068 Dick, Josef; Matsumoto, Makoto 9 2013 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. Zbl 1282.65007 1 2013 Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Zbl 1244.65002 Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich 22 2012 Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003 Aistleitner, C.; Brauchart, J. S.; Dick, J. 21 2012 Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003 Brauchart, Johann S.; Dick, Josef 10 2012 Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm. Zbl 1264.65030 Dick, Josef 3 2012 Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077 Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk 36 2011 Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011 Dick, Josef 15 2011 Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003 Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich 13 2011 Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010 Chen, S.; Dick, J.; Owen, A. B. 12 2011 Duality theory and propagation rules for higher order nets. Zbl 1229.11103 Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 6 2011 A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010 Baldeaux, Jan; Dick, Josef 3 2011 Quasi-Monte Carlo numerical integration on \(\mathbb {R}^s\): digital nets and worst-case error. Zbl 1236.11066 Dick, Josef 1 2011 Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012 Dick, Josef; Pillichshammer, Friedrich 341 2010 Duality theory and propagation rules for generalized digital nets. Zbl 1219.11115 Dick, Josef; Kritzer, Peter 11 2010 A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071 Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 3 2010 The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027 Dick, Josef 20 2009 QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005 Baldeaux, Jan; Dick, Josef 18 2009 On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004 Dick, Josef 15 2009 Equidistribution properties of generalized nets and sequences. Zbl 1228.65007 Dick, Josef; Baldeaux, Jan 9 2009 A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017 Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J. 2 2009 On the approximation of smooth functions using generalized digital nets. Zbl 1182.65024 Baldeaux, Jan; Dick, Josef; Kritzer, Peter 2 2009 Duality for digital sequences. Zbl 1181.11049 Dick, Josef; Niederreiter, Harald 1 2009 Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. Zbl 1189.42012 Dick, Josef 75 2008 The construction of good extensible rank-1 lattices. Zbl 1211.11092 Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. 21 2008 On the exact \(t\)-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031 Dick, Josef; Niederreiter, Harald 8 2008 Approximation of functions using digital nets. Zbl 1153.65314 Dick, Josef; Kritzer, Peter; Kuo, Frances Y. 4 2008 Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095 Dick, Josef 4 2008 An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316 Hickernell, Fred J.; Dick, Josef 1 2008 Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Zbl 1158.65007 Dick, Josef 44 2007 Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005 Dick, Josef; Pillichshammer, Friedrich 22 2007 Lattice-Nyström method for Fredholm integral equations of the second kind with convolution type kernels. Zbl 1131.65108 Dick, Josef; Kritzer, Peter; Kuo, Frances Y.; Sloan, Ian H. 9 2007 A note on the existence of sequences with small star discrepancy. Zbl 1132.11041 Dick, Josef 8 2007 The construction of extensible polynomial lattice rules with small weighted star discrepancy. Zbl 1135.11039 Dick, Josef 7 2007 On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047 Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 7 2007 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002 Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 6 2007 The construction of good extensible Korobov rules. Zbl 1131.11051 Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 3 2007 Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039 Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 3 2007 Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006 Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 1 2007 Good lattice rules in weighted Korobov spaces with general weights. Zbl 1097.65004 Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk 62 2006 Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023 Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich 9 2006 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025 Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 5 2006 A Taylor space for multivariate integration. Zbl 1103.65007 Dick, Josef 5 2006 ...and 15 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 764 Authors 81 Dick, Josef 81 Pillichshammer, Friedrich 52 Kritzer, Peter 45 Kuo, Frances Y. 40 Sloan, Ian Hugh 35 Schwab, Christoph 31 Nuyens, Dirk 28 Goda, Takashi 26 Woźniakowski, Henryk 21 Hinrichs, Aicke 19 Owen, Art B. 17 Gnewuch, Michael 17 Wasilkowski, Grzegorz W. 16 Suzuki, Kosuke 14 Hofer, Roswitha 14 Steinerberger, Stefan 13 Larchner, Gerhard 13 L’Ecuyer, Pierre 13 Lemieux, Christiane 13 Wang, Xiaoqun 13 Yoshiki, Takehito 12 Aistleitner, Christoph 12 Kritzinger, Ralph 12 Ullrich, Mario 11 Hickernell, Fred J. 11 Leobacher, Gunther 10 Brauchart, Johann S. 10 Cools, Ronald 10 Niederreiter, Harald 10 Pausinger, Florian 10 Potts, Daniel 10 Xu, Guiqiao 9 Faure, Henri 9 Herrmann, Lukas 9 Leovey, Hernan 9 Scheichl, Robert 8 He, Zhijian 8 Kämmerer, Lutz 8 Matsumoto, Makoto 8 Zech, Jakob 7 Bilyk, Dmitry 7 Liu, Yongping 7 Markhasin, Lev 7 Ullrich, Tino 7 Wang, Heping 6 Baldeaux, Jan 6 Ebert, Adrian 6 Gantner, Robert Nicholas 6 Gerber, Mathieu 6 Gilbert, Alexander D. 6 Irrgeher, Christian 6 Nobile, Fabio 6 Puchhammer, Florian 6 Ritter, Klaus 6 Römisch, Werner 6 Rudolf, Daniel 6 Sinescu, Vasile 6 Volkmer, Toni 6 Wang, Yuguang 6 Waterhouse, Benjamin J. 6 Werschulz, Arthur G. 6 Zhang, Jie 5 Basu, Kinjal 5 Ganesh, Mahadevan 5 Glaubitz, Jan 5 Griebel, Michael 5 Harbrecht, Helmut 5 Hefter, Mario 5 Heitsch, Holger 5 Le Gia, Quoc Thong 5 Levin, Mordekhaĭ Borisovich 5 Novak, Erich 5 Suryanarayana, Gowri 5 Travaglini, Giancarlo 5 Venturi, Daniele 5 Zhu, Houying 4 Beltrán, Carlos E. 4 Brandolini, Luca 4 Chen, Peng 4 Colzani, Leonardo 4 Dinh Dũng 4 Doerr, Benjamin 4 Dolgov, Sergey V. 4 Feischl, Michael 4 Gigante, Giacomo 4 Girolami, Mark A. 4 Graham, Ivan G. 4 Harase, Shin 4 Henrion, René 4 Jiménez Rugama, Lluís Antoni 4 Joe, Stephen 4 Klein, Thierry E. 4 Lagnoux, Agnès 4 Mhaskar, Hrushikesh N. 4 Multerer, Michael D. 4 Oates, Chris J. 4 Oettershagen, Jens 4 Osisiogu, Onyekachi 4 Schillings, Claudia 4 Skriganov, Maxim M. ...and 664 more Authors all top 5 Cited in 179 Serials 123 Journal of Complexity 39 Mathematics of Computation 30 SIAM Journal on Numerical Analysis 25 Journal of Computational and Applied Mathematics 22 SIAM/ASA Journal on Uncertainty Quantification 21 Journal of Approximation Theory 20 Numerische Mathematik 17 Monatshefte für Mathematik 16 Constructive Approximation 15 Mathematics and Computers in Simulation 13 SIAM Journal on Scientific Computing 12 Foundations of Computational Mathematics 11 Journal of Computational Physics 11 Monte Carlo Methods and Applications 11 Statistics and Computing 9 Finite Fields and their Applications 8 Computer Methods in Applied Mechanics and Engineering 8 Journal of Mathematical Analysis and Applications 8 The Annals of Statistics 8 Journal of Machine Learning Research (JMLR) 7 Computers & Mathematics with Applications 7 Computer Physics Communications 7 Acta Arithmetica 7 The Journal of Fourier Analysis and Applications 7 Electronic Journal of Statistics 6 Journal of Number Theory 6 Numerical Algorithms 6 SIAM Review 6 Journal de Théorie des Nombres de Bordeaux 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Archiv der Mathematik 5 Mathematika 5 Advances in Computational Mathematics 4 Discrete Mathematics 4 Functiones et Approximatio. 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Analysis and Computations 2 Research in the Mathematical Sciences 2 Results in Applied Mathematics 1 Archive for Rational Mechanics and Analysis 1 Discrete Applied Mathematics 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematische Semesterberichte 1 Periodica Mathematica Hungarica 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Biometrics 1 Hiroshima Mathematical Journal 1 Information Sciences 1 Integral Equations and Operator Theory 1 Journal of the American Statistical Association 1 Journal of Functional Analysis 1 Journal of Multivariate Analysis ...and 79 more Serials all top 5 Cited in 49 Fields 546 Numerical analysis (65-XX) 234 Number theory (11-XX) 152 Approximations and expansions (41-XX) 111 Statistics (62-XX) 83 Probability theory and stochastic processes (60-XX) 78 Partial differential equations (35-XX) 63 Computer science (68-XX) 54 Harmonic analysis on Euclidean spaces (42-XX) 50 Functional analysis (46-XX) 32 Operations research, mathematical programming (90-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Information and communication theory, circuits (94-XX) 17 Combinatorics (05-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 14 Real functions (26-XX) 12 Potential theory (31-XX) 10 Operator theory (47-XX) 10 Mechanics of deformable solids (74-XX) 10 Fluid mechanics (76-XX) 9 Integral equations (45-XX) 9 Convex and discrete geometry (52-XX) 9 Quantum theory (81-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Biology and other natural sciences (92-XX) 7 Measure and integration (28-XX) 7 Special functions (33-XX) 7 Systems theory; control (93-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Geometry (51-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Optics, electromagnetic theory (78-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 Ordinary differential equations (34-XX) 2 Difference and functional equations (39-XX) 2 Abstract harmonic analysis (43-XX) 2 Differential geometry (53-XX) 2 Geophysics (86-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) Citations by Year