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Author ID: dick.josef Recent zbMATH articles by "Dick, Josef"
Published as: Dick, Josef; Dick, J.
Homepage: https://web.maths.unsw.edu.au/~josefdick/
External Links: MGP · ORCID · Google Scholar
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

Publications by Year

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
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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
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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. Commentarii Mathematici
4 Proceedings of the American Mathematical Society
4 Applied Numerical Mathematics
4 European Journal of Operational Research
4 Mathematical Programming. Series A. Series B
4 Bernoulli
4 Quantitative Finance
4 Uniform Distribution Theory
4 Journal of Computational and Graphical Statistics
3 Bulletin of the Australian Mathematical Society
3 Inverse Problems
3 Advances in Mathematics
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Transactions of the American Mathematical Society
3 Statistical Science
3 Discrete & Computational Geometry
3 Journal of Scientific Computing
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Indagationes Mathematicae. New Series
3 Applied and Computational Harmonic Analysis
3 The ANZIAM Journal
3 International Journal of Wavelets, Multiresolution and Information Processing
3 GEM - International Journal on Geomathematics
3 Bayesian Analysis
2 Journal of Statistical Physics
2 Physics Reports
2 Bulletin of Mathematical Biology
2 BIT
2 Computing
2 Journal of Applied Probability
2 Mathematische Nachrichten
2 Mathematics of Operations Research
2 Operations Research
2 Statistics & Probability Letters
2 Operations Research Letters
2 Acta Applicandae Mathematicae
2 Computational Mechanics
2 The Annals of Applied Probability
2 International Journal of Computer Mathematics
2 Computational Optimization and Applications
2 Methodology and Computing in Applied Probability
2 Acta Mathematica Scientia. Series B. (English Edition)
2 Acta Numerica
2 Communications in Computational Physics
2 Science China. Mathematics
2 Journal of Probability and Statistics
2 Stochastic and Partial Differential Equations. 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
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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)

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