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## Dick, Josef

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 Author ID: dick.josef Published as: Dick, J.; Dick, Josef External Links: MGP · ORCID
 Documents Indexed: 113 Publications since 2004, including 4 Books
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#### Co-Authors

 15 single-authored 42 Pillichshammer, Friedrich 13 Kritzer, Peter 10 Kuo, Frances Y. 8 Baldeaux, Jan 8 Leobacher, Gunther 8 Schwab, Christoph 7 Le Gia, Quoc Thong 6 Sloan, Ian Hugh 5 Brauchart, Johann S. 5 Hinrichs, Aicke 5 Woźniakowski, Henryk 5 Zhu, Houying 4 Goda, Takashi 4 Yoshiki, Takehito 3 Aistleitner, Christoph 3 Niederreiter, Harald 3 Nuyens, Dirk 3 Rudolf, Daniel 3 Suzuki, Kosuke 3 Wang, Xiaoqun 2 Chen, Su 2 Cristea, Ligia-Loreta 2 Gantner, Robert Nicholas 2 Gnewuch, Michael 2 Hickernell, Fred J. 2 Markhasin, Lev 2 Owen, Art B. 2 Ullrich, Mario 2 Waterhouse, Benjamin J. 1 Bilyk, Dmitry 1 Fang, Lou 1 Feischl, Michael 1 Gomez-Perez, Domingo 1 Greslehner, Julia 1 Irrgeher, Christian 1 Larcher, Gerhard 1 Liu, Kwong-Ip 1 Matsumoto, Makoto 1 Peters, Gareth William 1 Pirsic, Isabel 1 Prochno, Joscha 1 Schmid, Wolfgang Ch. 1 Winterhof, Arne
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#### Serials

 16 Journal of Complexity 11 SIAM Journal on Numerical Analysis 7 Numerische Mathematik 6 Mathematics of Computation 4 Acta Arithmetica 3 Journal of Computational and Applied Mathematics 3 Proceedings of the American Mathematical Society 3 Finite Fields and their Applications 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Statistics 2 Archiv der Mathematik 2 Journal of Approximation Theory 2 Constructive Approximation 2 Numerical Algorithms 2 Monte Carlo Methods and Applications 2 Foundations of Computational Mathematics 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 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 Uniform Distribution Theory 1 Electronic Journal of Statistics 1 Radon Series on Computational and Applied Mathematics 1 Statistics and Computing 1 Information and Inference 1 Springer Proceedings in Mathematics & Statistics 1 SIAM/ASA Journal on Uncertainty Quantification
all top 5

#### Fields

 85 Numerical analysis (65-XX) 68 Number theory (11-XX) 13 Approximations and expansions (41-XX) 11 Probability theory and stochastic processes (60-XX) 9 Functional analysis (46-XX) 9 Statistics (62-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 3 General and overarching topics; collections (00-XX) 3 Partial differential equations (35-XX) 2 Real functions (26-XX) 2 Integral equations (45-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 Operator theory (47-XX) 1 Computer science (68-XX)

#### Citations contained in zbMATH

100 Publications have been cited 1,377 times in 532 Documents Cited by Year
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
2010
High-dimensional integration: The quasi-Monte Carlo way. Zbl 1296.65004
Dick, Josef; Kuo, Frances Y.; Sloan, Ian H.
2013
Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. Zbl 1189.42012
Dick, Josef
2008
Good lattice rules in weighted Korobov spaces with general weights. Zbl 1097.65004
Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk
2006
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021
Dick, Josef; Pillichshammer, Friedrich
2005
Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Zbl 1158.65007
Dick, Josef
2007
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
2014
On the convergence rate of the component-by-component construction of good lattice rules. Zbl 1344.65034
Dick, Josef
2004
Liberating the weights. Zbl 1089.65005
Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk
2004
Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H.
2005
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
2011
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
2014
Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph
2017
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
2008
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
2016
Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002
Goda, Takashi; Dick, Josef
2015
The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027
Dick, Josef
2009
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
2007
Point sets on the sphere $$\mathbb{S}^{2}$$ with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J.
2012
Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031
Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph
2016
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038
Aistleitner, Christoph; Dick, Josef
2015
QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005
Baldeaux, Jan; Dick, Josef
2009
A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, Johann S.; Dick, Josef
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
2012
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
2014
On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004
Dick, Josef
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
2005
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
2014
Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. Zbl 1296.41025
Dick, Josef; Gnewuch, Michael
2014
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011
Dick, Josef
2011
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
2011
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2005
Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. Zbl 1312.65002
Dick, Josef; Gnewuch, Michael
2014
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
2014
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
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
2013
Duality theory and propagation rules for generalized digital nets. Zbl 1219.11115
Dick, Josef; Kritzer, Peter
2010
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
2006
On Korobov lattice rules in weighted spaces. Zbl 1079.65010
Wang, Xiaoqun; Sloan, Ian H.; Dick, Josef
2004
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.
2015
Discrepancy bounds for infinite-dimensional order two digital sequences over $$\mathbb F_2$$. Zbl 1286.11120
Dick, Josef
2014
Equidistribution properties of generalized nets and sequences. Zbl 1228.65007
Dick, Josef; Baldeaux, Jan
2009
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.
2007
The weighted star discrepancy of Korobov’s $$p$$-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
2015
Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079
Aistleitner, Christoph; Dick, Josef
2014
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010
Chen, S.; Dick, J.; Owen, A. B.
2011
The construction of extensible polynomial lattice rules with small weighted star discrepancy. Zbl 1135.11039
Dick, Josef
2007
Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003
Dick, Josef; Pillichshammer, Friedrich
2005
Reducing the construction cost of the component-by-component construction of good lattice rules. Zbl 1051.65003
Dick, J.; Kuo, F. Y.
2004
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
2015
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou
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
2015
Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113
Zhu, Houying; Dick, Josef
2014
Quasi-Monte Carlo rules for numerical integration over the unit sphere $${\mathbb{S}^2}$$. Zbl 1258.65003
Brauchart, Johann S.; Dick, Josef
2012
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2011
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.
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
2007
On the exact $$t$$-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031
Dick, Josef; Niederreiter, Harald
2008
A note on the existence of sequences with small star discrepancy. Zbl 1132.11041
Dick, Josef
2007
A best possible upper bound on the star discrepancy of $$(t,m,2)$$-nets. Zbl 1103.11022
Dick, Josef; Kritzer, Peter
2006
A Taylor space for multivariate integration. Zbl 1103.65007
Dick, Josef
2006
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. Zbl 1351.60100
Dick, Josef; Rudolf, Daniel; Zhu, Houying
2016
On a projection-corrected component-by-component construction. Zbl 1329.65007
Dick, Josef; Kritzer, Peter
2016
Higher order Sobol’ indices. Zbl 1309.62098
Owen, Art B.; Dick, Josef; Chen, Su
2014
Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013
Dick, Josef
2014
Approximation of functions using digital nets. Zbl 1153.65314
Dick, Josef; Kritzer, Peter; Kuo, Frances Y.
2008
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
2006
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.
2005
Constructing good lattice rules with millions of points. Zbl 1043.65002
Dick, Josef; Kuo, Frances Y.
2004
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
Optimal $$L_{p}$$-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
Fast QMC matrix-vector multiplication. Zbl 1320.65008
Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph
2015
A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010
Baldeaux, Jan; Dick, Josef
2011
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2010
Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095
Dick, Josef
2008
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
2007
Dyadic diaphony of digital nets over $$\mathbb Z_2$$. Zbl 1130.11042
Dick, Josef; Pillichshammer, Friedrich
2005
Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359
Dick, Josef; Feischl, Michael; Schwab, Christoph
2019
Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010
Dick, Josef (ed.); Kuo, Frances Y. (ed.); Woźniakowski, Henryk (ed.)
2018
Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Zbl 1385.65002
Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito
2017
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2014
Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo. Zbl 1309.65004
Dick, Josef; Rudolf, Daniel
2014
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
Dick, Josef (ed.); Kuo, Frances Y. (ed.); Peters, Gareth W. (ed.); Sloan, Ian H. (ed.)
2013
Random weights, robust lattice rules and the geometry of the $$cbcrc$$ algorithm. Zbl 1264.65030
Dick, Josef
2012
A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J.
2009
On the approximation of smooth functions using generalized digital nets. Zbl 1182.65024
Baldeaux, Jan; Dick, Josef; Kritzer, Peter
2009
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph
2019
A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005
Dick, Josef; Rudolf, Daniel; Zhu, Houying
2019
Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058
Dick, Josef; Goda, Takashi; Yoshiki, Takehito
2019
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
2017
Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017
Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph
2015
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
Applications of geometric discrepancy in numerical analysis and statistics. Zbl 1368.11077
Dick, Josef
2014
Duality for digital sequences. Zbl 1181.11049
Dick, Josef; Niederreiter, Harald
2009
An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316
Hickernell, Fred J.; Dick, Josef
2008
Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Periodic functions with bounded remainder. Zbl 1115.11044
Dick, Josef; Pillichshammer, Friedrich
2006
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
2006
Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359
Dick, Josef; Feischl, Michael; Schwab, Christoph
2019
Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph
2019
A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005
Dick, Josef; Rudolf, Daniel; Zhu, Houying
2019
Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058
Dick, Josef; Goda, Takashi; Yoshiki, Takehito
2019
Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010
Dick, Josef (ed.); Kuo, Frances Y. (ed.); Woźniakowski, Henryk (ed.)
2018
Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph
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
2017
Optimal $$L_{p}$$-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Zbl 1385.65002
Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito
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
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
2016
Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031
Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph
2016
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. Zbl 1351.60100
Dick, Josef; Rudolf, Daniel; Zhu, Houying
2016
On a projection-corrected component-by-component construction. Zbl 1329.65007
Dick, Josef; Kritzer, Peter
2016
Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002
Goda, Takashi; Dick, Josef
2015
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038
Aistleitner, Christoph; Dick, Josef
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.
2015
The weighted star discrepancy of Korobov’s $$p$$-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
2015
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
2015
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou
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
2015
Fast QMC matrix-vector multiplication. Zbl 1320.65008
Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph
2015
Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017
Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph
2015
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
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
2014
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
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
2014
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
2014
Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. Zbl 1296.41025
Dick, Josef; Gnewuch, Michael
2014
Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. Zbl 1312.65002
Dick, Josef; Gnewuch, Michael
2014
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
2014
Discrepancy bounds for infinite-dimensional order two digital sequences over $$\mathbb F_2$$. Zbl 1286.11120
Dick, Josef
2014
Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079
Aistleitner, Christoph; Dick, Josef
2014
Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113
Zhu, Houying; Dick, Josef
2014
Higher order Sobol’ indices. Zbl 1309.62098
Owen, Art B.; Dick, Josef; Chen, Su
2014
Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013
Dick, Josef
2014
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2014
Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo. Zbl 1309.65004
Dick, Josef; Rudolf, Daniel
2014
Applications of geometric discrepancy in numerical analysis and statistics. Zbl 1368.11077
Dick, Josef
2014
High-dimensional integration: The quasi-Monte Carlo way. Zbl 1296.65004
Dick, Josef; Kuo, Frances Y.; Sloan, Ian H.
2013
A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, Johann S.; Dick, Josef
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
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
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
Dick, Josef (ed.); Kuo, Frances Y. (ed.); Peters, Gareth W. (ed.); Sloan, Ian H. (ed.)
2013
Point sets on the sphere $$\mathbb{S}^{2}$$ with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J.
2012
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
2012
Quasi-Monte Carlo rules for numerical integration over the unit sphere $${\mathbb{S}^2}$$. Zbl 1258.65003
Brauchart, Johann S.; Dick, Josef
2012
Random weights, robust lattice rules and the geometry of the $$cbcrc$$ algorithm. Zbl 1264.65030
Dick, Josef
2012
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
2011
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011
Dick, Josef
2011
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
2011
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010
Chen, S.; Dick, J.; Owen, A. B.
2011
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2011
A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010
Baldeaux, Jan; Dick, Josef
2011
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
2010
Duality theory and propagation rules for generalized digital nets. Zbl 1219.11115
Dick, Josef; Kritzer, Peter
2010
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2010
The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027
Dick, Josef
2009
QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005
Baldeaux, Jan; Dick, Josef
2009
On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004
Dick, Josef
2009
Equidistribution properties of generalized nets and sequences. Zbl 1228.65007
Dick, Josef; Baldeaux, Jan
2009
A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J.
2009
On the approximation of smooth functions using generalized digital nets. Zbl 1182.65024
Baldeaux, Jan; Dick, Josef; Kritzer, Peter
2009
Duality for digital sequences. Zbl 1181.11049
Dick, Josef; Niederreiter, Harald
2009
Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. Zbl 1189.42012
Dick, Josef
2008
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
2008
On the exact $$t$$-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031
Dick, Josef; Niederreiter, Harald
2008
Approximation of functions using digital nets. Zbl 1153.65314
Dick, Josef; Kritzer, Peter; Kuo, Frances Y.
2008
Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095
Dick, Josef
2008
An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316
Hickernell, Fred J.; Dick, Josef
2008
Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Zbl 1158.65007
Dick, Josef
2007
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
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.
2007
The construction of extensible polynomial lattice rules with small weighted star discrepancy. Zbl 1135.11039
Dick, Josef
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.
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
2007
A note on the existence of sequences with small star discrepancy. Zbl 1132.11041
Dick, Josef
2007
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
2007
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Good lattice rules in weighted Korobov spaces with general weights. Zbl 1097.65004
Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk
2006
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
2006
A best possible upper bound on the star discrepancy of $$(t,m,2)$$-nets. Zbl 1103.11022
Dick, Josef; Kritzer, Peter
2006
A Taylor space for multivariate integration. Zbl 1103.65007
Dick, Josef
2006
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
2006
Periodic functions with bounded remainder. Zbl 1115.11044
Dick, Josef; Pillichshammer, Friedrich
2006
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
2006
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021
Dick, Josef; Pillichshammer, Friedrich
2005
Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H.
2005
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
2005
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2005
Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003
Dick, Josef; Pillichshammer, Friedrich
2005
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.
2005
Dyadic diaphony of digital nets over $$\mathbb Z_2$$. Zbl 1130.11042
Dick, Josef; Pillichshammer, Friedrich
2005
On the convergence rate of the component-by-component construction of good lattice rules. Zbl 1344.65034
Dick, Josef
2004
Liberating the weights. Zbl 1089.65005
Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk
2004
On Korobov lattice rules in weighted spaces. Zbl 1079.65010
Wang, Xiaoqun; Sloan, Ian H.; Dick, Josef
2004
Reducing the construction cost of the component-by-component construction of good lattice rules. Zbl 1051.65003
Dick, J.; Kuo, F. Y.
2004
Constructing good lattice rules with millions of points. Zbl 1043.65002
Dick, Josef; Kuo, Frances Y.
2004
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#### Cited by 491 Authors

 71 Dick, Josef 68 Pillichshammer, Friedrich 46 Kritzer, Peter 36 Kuo, Frances Y. 33 Sloan, Ian Hugh 28 Schwab, Christoph 25 Woźniakowski, Henryk 21 Nuyens, Dirk 20 Goda, Takashi 18 Hinrichs, Aicke 16 Wasilkowski, Grzegorz W. 13 Suzuki, Kosuke 12 Gnewuch, Michael 12 Hofer, Roswitha 12 Larcher, Gerhard 12 Steinerberger, Stefan 12 Yoshiki, Takehito 11 Hickernell, Fred J. 11 Owen, Art B. 10 Aistleitner, Christoph 10 Brauchart, Johann S. 10 Leobacher, Gunther 10 Wang, Xiaoqun 9 Niederreiter, Harald 9 Scheichl, Robert 8 Cools, Ronald 8 Pausinger, Florian 8 Ullrich, Mario 8 Xu, Guiqiao 7 Faure, Henri 7 Herrmann, Lukas 7 Kritzinger, Ralph 7 Lemieux, Christiane 7 Leovey, Hernan 7 Markhasin, Lev 7 Zech, Jakob 6 Baldeaux, Jan 6 Gantner, Robert Nicholas 6 He, Zhijian 6 Irrgeher, Christian 6 L’Ecuyer, Pierre 6 Potts, Daniel 6 Werschulz, Arthur G. 5 Basu, Kinjal 5 Bilyk, Dmitry 5 Griebel, Michael 5 Heitsch, Holger 5 Kämmerer, Lutz 5 Liu, Yongping 5 Ritter, Klaus 5 Sinescu, Vasile 5 Suryanarayana, Gowri 5 Volkmer, Toni 5 Waterhouse, Benjamin J. 5 Zhu, Houying 4 Ganesh, Mahadevan 4 Gerber, Mathieu 4 Graham, Ivan G. 4 Harase, Shin 4 Hefter, Mario 4 Jiménez Rugama, Lluís Antoni 4 Le Gia, Quoc Thong 4 Matsumoto, Makoto 4 Schillings, Claudia 4 Ullrich, Tino 4 Wang, Heping 4 Wang, Yuguang 3 Beltrán, Carlos 3 Brandolini, Luca 3 Chen, Peng 3 Colzani, Leonardo 3 Doerr, Benjamin 3 Gigante, Giacomo 3 Gilbert, Alexander D. 3 Griewank, Andreas 3 Henrion, René 3 Mhaskar, Hrushikesh N. 3 Nobile, Fabio 3 Oettershagen, Jens 3 Ohori, Ryuichi 3 Papageorgiou, Anargyros 3 Römisch, Werner 3 Rudolf, Daniel 3 Skriganov, Maxim M. 3 Tezuka, Shu 3 Tichy, Robert Franz 3 Travaglini, Giancarlo 3 Vandewalle, Stefan G. 3 Venturi, Daniele 3 Womersley, Robert S. 2 Ammon, A. 2 Bornn, Luke 2 Briol, François-Xavier 2 Brown, Louis 2 Chen, Jia 2 Cristea, Ligia-Loreta 2 Dai, Feng 2 Dinh Dũng 2 Dolgov, Sergey V. 2 Drovandi, Christopher C. ...and 391 more Authors
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#### Cited in 125 Serials

 97 Journal of Complexity 28 Mathematics of Computation 21 SIAM Journal on Numerical Analysis 19 Journal of Approximation Theory 18 Journal of Computational and Applied Mathematics 16 Numerische Mathematik 16 SIAM/ASA Journal on Uncertainty Quantification 12 Monatshefte für Mathematik 11 Constructive Approximation 10 Foundations of Computational Mathematics 9 Finite Fields and their Applications 8 SIAM Journal on Scientific Computing 8 Monte Carlo Methods and Applications 8 Statistics and Computing 6 Journal of Computational Physics 6 Journal of Number Theory 5 Computers & Mathematics with Applications 5 Journal of Mathematical Analysis and Applications 5 The Annals of Statistics 5 Mathematics and Computers in Simulation 5 Numerical Algorithms 5 Journal de Théorie des Nombres de Bordeaux 5 The Journal of Fourier Analysis and Applications 4 Acta Arithmetica 4 Functiones et Approximatio. Commentarii Mathematici 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Bulletin of the Australian Mathematical Society 3 Computer Physics Communications 3 Discrete Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Archiv der Mathematik 3 Mathematika 3 Proceedings of the American Mathematical Society 3 Applied Numerical Mathematics 3 Statistical Science 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Review 3 Indagationes Mathematicae. New Series 3 Applied and Computational Harmonic Analysis 3 Advances in Computational Mathematics 3 The ANZIAM Journal 3 Electronic Journal of Statistics 3 GEM - International Journal on Geomathematics 2 Inverse Problems 2 Journal of Statistical Physics 2 Advances in Mathematics 2 Computing 2 Journal of Applied Probability 2 Journal of Statistical Planning and Inference 2 Mathematische Nachrichten 2 Operations Research 2 Transactions of the American Mathematical Society 2 Statistics & Probability Letters 2 Operations Research Letters 2 Acta Applicandae Mathematicae 2 European Journal of Operational Research 2 International Journal of Computer Mathematics 2 Computational Optimization and Applications 2 Quantitative Finance 2 Journal of Machine Learning Research (JMLR) 2 International Journal of Wavelets, Multiresolution and Information Processing 2 Bayesian Analysis 1 Computer Methods in Applied Mechanics and Engineering 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 Periodica Mathematica Hungarica 1 Physics Letters. A 1 Physics Reports 1 Bulletin of Mathematical Biology 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Biometrics 1 BIT 1 Journal of Optimization Theory and Applications 1 Mathematics of Operations Research 1 Mathematische Zeitschrift 1 Optimization 1 Probability Theory and Related Fields 1 Discrete & Computational Geometry 1 Journal of Integral Equations and Applications 1 Science in China. Series A 1 Annals of Operations Research 1 The Annals of Applied Probability 1 The Journal of Geometric Analysis 1 Journal of Global Optimization 1 Designs, Codes and Cryptography 1 Linear Algebra and its Applications 1 SIAM Journal on Mathematical Analysis 1 Stochastic Processes and their Applications 1 Mathematical Programming. Series A. Series B 1 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică 1 SIAM Journal on Optimization 1 Journal of Mathematical Imaging and Vision 1 Russian Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Bernoulli 1 Finance and Stochastics ...and 25 more Serials
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#### Cited in 42 Fields

 374 Numerical analysis (65-XX) 172 Number theory (11-XX) 103 Approximations and expansions (41-XX) 63 Statistics (62-XX) 56 Probability theory and stochastic processes (60-XX) 52 Partial differential equations (35-XX) 43 Functional analysis (46-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 32 Computer science (68-XX) 21 Operations research, mathematical programming (90-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Real functions (26-XX) 9 Information and communication theory, circuits (94-XX) 8 Combinatorics (05-XX) 7 Integral equations (45-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Operator theory (47-XX) 6 Convex and discrete geometry (52-XX) 6 Quantum theory (81-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Fluid mechanics (76-XX) 4 Measure and integration (28-XX) 4 Potential theory (31-XX) 4 Special functions (33-XX) 4 Mechanics of deformable solids (74-XX) 4 Biology and other natural sciences (92-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Geometry (51-XX) 3 Optics, electromagnetic theory (78-XX) 3 Systems theory; control (93-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Geophysics (86-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Topological groups, Lie groups (22-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX)