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
|
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
|
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
|
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
|
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk |
|
2014
|
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
|
Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph |
|
2017
|
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich |
|
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 |
|
2016
|
Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031
Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph |
|
2016
|
A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, Johann S.; Dick, Josef |
|
2013
|
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038
Aistleitner, Christoph; Dick, Josef |
|
2015
|
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
|
Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J. |
|
2012
|
Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002
Goda, Takashi; Dick, Josef |
|
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 |
|
2012
|
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. |
|
2008
|
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich |
|
2007
|
The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027
Dick, Josef |
|
2009
|
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich |
|
2014
|
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
|
QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005
Baldeaux, Jan; Dick, Josef |
|
2009
|
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
|
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich |
|
2005
|
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011
Dick, Josef |
|
2011
|
On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004
Dick, Josef |
|
2009
|
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich |
|
2015
|
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich |
|
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. |
|
2015
|
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010
Chen, S.; Dick, J.; Owen, A. B. |
|
2011
|
Lattice rules. Numerical integration, approximation, and discrepancy. Zbl 07566616
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich |
|
2022
|
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
|
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
|
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich |
|
2011
|
Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\). Zbl 1286.11120
Dick, Josef |
|
2014
|
On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953
Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich |
|
2018
|
The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich |
|
2015
|
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 generalized digital nets. Zbl 1219.11115
Dick, Josef; Kritzer, Peter |
|
2010
|
On Korobov lattice rules in weighted spaces. Zbl 1079.65010
Wang, Xiaoqun; Sloan, Ian H.; Dick, Josef |
|
2004
|
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
|
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
|
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich |
|
2006
|
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. Zbl 1484.65005
Dick, Josef; Goda, Takashi |
|
2021
|
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
|
Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013
Dick, Josef |
|
2014
|
Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079
Aistleitner, Christoph; Dick, Josef |
|
2014
|
Higher order Sobol’ indices. Zbl 1309.62098
Owen, Art B.; Dick, Josef; Chen, Su |
|
2014
|
A note on the existence of sequences with small star discrepancy. Zbl 1132.11041
Dick, Josef |
|
2007
|
On the exact \(t\)-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031
Dick, Josef; Niederreiter, Harald |
|
2008
|
Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010
|
|
2018
|
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. |
|
2019
|
Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113
Zhu, Houying; Dick, Josef |
|
2014
|
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
|
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
|
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
|
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich |
|
2011
|
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou |
|
2015
|
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich |
|
2006
|
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
|
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
|
A Taylor space for multivariate integration. Zbl 1103.65007
Dick, Josef |
|
2006
|
A best possible upper bound on the star discrepancy of \((t,m,2)\)-nets. Zbl 1103.11022
Dick, Josef; Kritzer, Peter |
|
2006
|
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 |
|
2022
|
Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359
Dick, Josef; Feischl, Michael; Schwab, Christoph |
|
2019
|
Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058
Dick, Josef; Goda, Takashi; Yoshiki, Takehito |
|
2019
|
Constructing good lattice rules with millions of points. Zbl 1043.65002
Dick, Josef; Kuo, Frances Y. |
|
2004
|
A note on the periodic \(L_2\)-discrepancy of Korobov’s \(p\)-sets. Zbl 1448.11148
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich |
|
2020
|
Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095
Dick, Josef |
|
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. |
|
2005
|
Approximation of functions using digital nets. Zbl 1153.65314
Dick, Josef; Kritzer, Peter; Kuo, Frances Y. |
|
2008
|
Periodic functions with bounded remainder. Zbl 1115.11044
Dick, Josef; Pillichshammer, Friedrich |
|
2006
|
Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Zbl 1385.65002
Dick, Josef; Goda, Takashi; Suzuki, Kosuke; Yoshiki, Takehito |
|
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
|
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
|
Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo. Zbl 1309.65004
Dick, Josef; Rudolf, Daniel |
|
2014
|
Dyadic diaphony of digital nets over \(\mathbb Z_2\). Zbl 1130.11042
Dick, Josef; Pillichshammer, Friedrich |
|
2005
|
A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010
Baldeaux, Jan; Dick, Josef |
|
2011
|
Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm. Zbl 1264.65030
Dick, Josef |
|
2012
|
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich |
|
2007
|
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J. |
|
2007
|
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
|
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich |
|
2010
|
A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005
Dick, Josef; Rudolf, Daniel; Zhu, Houying |
|
2019
|
A quasi-Monte Carlo data compression algorithm for machine learning. Zbl 07418854
Dick, Josef; Feischl, Michael |
|
2021
|
Applications of geometric discrepancy in numerical analysis and statistics. Zbl 1368.11077
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
|
A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J. |
|
2009
|
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 |
|
2023
|
Lattice rules. Numerical integration, approximation, and discrepancy. Zbl 07566616
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich |
|
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 |
|
2022
|
Extrapolated polynomial lattice rule integration in computational uncertainty quantification. Zbl 1494.65004
Dick, Josef; Longo, Marcello; Schwab, Christoph |
|
2022
|
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. Zbl 1484.65005
Dick, Josef; Goda, Takashi |
|
2021
|
A quasi-Monte Carlo data compression algorithm for machine learning. Zbl 07418854
Dick, Josef; Feischl, Michael |
|
2021
|
Weighted integration over a hyperrectangle based on digital nets and sequences. Zbl 1467.65019
Dick, Josef; Pillichshammer, Friedrich |
|
2021
|
A note on the periodic \(L_2\)-discrepancy of Korobov’s \(p\)-sets. Zbl 1448.11148
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich |
|
2020
|
Tractability properties of the discrepancy in Orlicz norms. Zbl 1470.46050
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich; Prochno, Joscha |
|
2020
|
Discrepancy theory. Zbl 1454.11006
|
|
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 |
|
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. |
|
2019
|
Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359
Dick, Josef; Feischl, Michael; Schwab, Christoph |
|
2019
|
Richardson extrapolation of polynomial lattice rules. Zbl 1415.65058
Dick, Josef; Goda, Takashi; Yoshiki, Takehito |
|
2019
|
A weighted discrepancy bound of quasi-Monte Carlo importance sampling. Zbl 1427.65005
Dick, Josef; Rudolf, Daniel; Zhu, Houying |
|
2019
|
On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953
Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich |
|
2018
|
Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Zbl 1398.65010
|
|
2018
|
Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. Zbl 1385.65003
Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito |
|
2018
|
Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169
Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph |
|
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
|
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
|
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
|
Discrepancy estimates for acceptance-rejection samplers using stratified inputs. Zbl 1356.65014
Zhu, Houying; Dick, Josef |
|
2016
|
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. Zbl 1326.11038
Aistleitner, Christoph; Dick, Josef |
|
2015
|
Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Zbl 1323.65002
Goda, Takashi; Dick, Josef |
|
2015
|
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich |
|
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
|
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
|
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou |
|
2015
|
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich |
|
2015
|
Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017
Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph |
|
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
|
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
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
|
Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\). Zbl 1286.11120
Dick, Josef |
|
2014
|
Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series. Zbl 1291.65013
Dick, Josef |
|
2014
|
Low-discrepancy point sets for non-uniform measures. Zbl 1300.11079
Aistleitner, Christoph; Dick, Josef |
|
2014
|
Higher order Sobol’ indices. Zbl 1309.62098
Owen, Art B.; Dick, Josef; Chen, Su |
|
2014
|
Discrepancy bounds for deterministic acceptance-rejection samplers. Zbl 1348.60113
Zhu, Houying; Dick, Josef |
|
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
|
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich |
|
2014
|
High-dimensional integration: The quasi-Monte Carlo way. Zbl 1296.65004
Dick, Josef; Kuo, Frances Y.; Sloan, Ian H. |
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2013
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A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, Johann S.; Dick, Josef |
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2013
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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 |
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2013
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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 |
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2013
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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
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2013
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Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J. |
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2012
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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 |
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2012
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Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003
Brauchart, Johann S.; Dick, Josef |
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2012
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Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm. Zbl 1264.65030
Dick, Josef |
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2012
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Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk |
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2011
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Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Zbl 1298.65011
Dick, Josef |
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2011
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Consistency of Markov chain quasi-Monte Carlo on continuous state spaces. Zbl 1225.65010
Chen, S.; Dick, J.; Owen, A. B. |
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2011
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Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich |
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2011
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Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich |
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2011
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A construction of polynomial lattice rules with small gain coefficients. Zbl 1298.65010
Baldeaux, Jan; Dick, Josef |
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2011
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Quasi-Monte Carlo numerical integration on \(\mathbb {R}^s\): digital nets and worst-case error. Zbl 1236.11066
Dick, Josef |
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2011
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Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich |
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2010
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Duality theory and propagation rules for generalized digital nets. Zbl 1219.11115
Dick, Josef; Kritzer, Peter |
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2010
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A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich |
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2010
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The decay of the Walsh coefficients of smooth functions. Zbl 1183.42027
Dick, Josef |
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2009
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QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Zbl 1186.65005
Baldeaux, Jan; Dick, Josef |
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2009
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On quasi-Monte Carlo rules achieving higher order convergence. Zbl 1184.65004
Dick, Josef |
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2009
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Equidistribution properties of generalized nets and sequences. Zbl 1228.65007
Dick, Josef; Baldeaux, Jan |
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2009
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A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J. |
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2009
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On the approximation of smooth functions using generalized digital nets. Zbl 1182.65024
Baldeaux, Jan; Dick, Josef; Kritzer, Peter |
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2009
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Duality for digital sequences. Zbl 1181.11049
Dick, Josef; Niederreiter, Harald |
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2009
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Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. Zbl 1189.42012
Dick, Josef |
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2008
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The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. |
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2008
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On the exact \(t\)-value of Niederreiter and Sobol’ sequences. Zbl 1156.11031
Dick, Josef; Niederreiter, Harald |
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2008
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Koksma-Hlawka type inequalities of fractional order. Zbl 1223.11095
Dick, Josef |
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2008
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Approximation of functions using digital nets. Zbl 1153.65314
Dick, Josef; Kritzer, Peter; Kuo, Frances Y. |
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2008
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An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316
Hickernell, Fred J.; Dick, Josef |
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2008
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Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Zbl 1158.65007
Dick, Josef |
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2007
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Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich |
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2007
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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. |
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2007
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A note on the existence of sequences with small star discrepancy. Zbl 1132.11041
Dick, Josef |
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2007
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The construction of extensible polynomial lattice rules with small weighted star discrepancy. Zbl 1135.11039
Dick, Josef |
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2007
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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. |
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2007
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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 |
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2007
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Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich |
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2007
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The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J. |
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2007
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Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich |
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2007
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Good lattice rules in weighted Korobov spaces with general weights. Zbl 1097.65004
Dick, Josef; Sloan, Ian H.; Wang, Xiaoqun; Woźniakowski, Henryk |
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2006
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Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich |
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2006
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Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich |
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2006
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A Taylor space for multivariate integration. Zbl 1103.65007
Dick, Josef |
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2006
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| ...and 15 more Documents |
