Professor Josef Dick

ABOUT ME

Biography

Dr Josef Dick is a Professor and Deputy Head in the School of Mathematics and Statistics, UNSW.

Education

- PhD in Mathematics, UNSW, 2004.
- MSc in Mathematics, Univeristy of Salzburg, 2001.

RESEARCH

Research in Detail

Dr Dick’s main research interests relate to numerical integration and, in particular, quasi-Monte Carlo rules. His research uses a variety of techniques from number theory, abstract algebra (finite fields in particular), discrepancy theory, wavelet theory and statistics, for the rigorous analysis of practical algorithms for computational problems. He also often provides implementation of his algorithms in Matlab to bridge the gap between theory and applications of his work. He has successfully applied his ideas to point distributions on the unit cube for use in numerical integration algorithms, completely uniformly distributed sequences for Markov chain quasi-Monte Carlo algorithms and, most recently, to explicit constructions of uniformly distributed points on the sphere.

Research Grants

- - Chief investigator for Discovery project from the Australian Research Council, 2012-2014 for the project ``Mathematics in the round - the challenge of computational analysis on spheres''. Chief Investigator (CI) Prof. Ian Sloan (UNSW), CI Dr. Josef Dick (UNSW), Partner investigator (PI) Prof. Holger Wendland (Oxford University), PI Prof. Ed B. Saff (Vanderbilt University).
  - Queen Elizabeth II Fellowship from the Australian Research Council, 2010-2014 for the project ``Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo''.
  - UNSW Vice Chancellor Fellowship 2006 - 2009.

Current Student Projects (PhD and Honours)

Quasi-Monte Carlo methods

Discrepancy Theory

Markov chain Monte Carlo

Uncertainty Quantification

Advice for prospective students

Please contact me via email if you are interested in working with me. It would be helpful if you could also describe your interests and background in numerical analysis, number theory, algebra, or statistics.

TEACHING & OUTREACH

Courses I teach

Math1151 Algebra

Math3311/5335 Mathematical Computing for Finance

Professional affiliations and service positions

Editor Journal of Complexity and Journal of Approximation Theory

Phone

9385 7040

E-mail

josef.dick@unsw.edu.au

Location

School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 2074

Books | 2022

Dick J; Kritzer P; Pillichshammer F, 2022, Lattice Rules, Springer International Publishing, http://dx.doi.org/10.1007/978-3-031-09951-9

Books | 2018

Sloan IH, 2018, A fortunate scientific life, http://dx.doi.org/10.1007/978-3-319-72456-0

Books | 2010

Pillichshammer F; Dick J, 2010, Digital Nets and Sequences - Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, Cambridge, http://dx.doi.org/10.1017/CBO9780511761188
Book Chapters | 2020

Bilyk D; Dick J; Pillichshammer F, 2020, 'Radon Series on Computational and Applied Mathematics Preface', in Bilyk D; Dick J; Pillichshammer F (ed.), DISCREPANCY THEORY, WALTER DE GRUYTER GMBH, pp. V - VII, http://dx.doi.org/10.1515/9783110652581-201

Book Chapters | 2014

Dick J, 2014, 'Applications of geometric discrepancy in numerical analysis and statistics', in Applied Algebra and Number Theory: Essays in Honor of Harald Niederreiter on the Occasion of his 70th Birthday, pp. 39 - 57, http://dx.doi.org/10.1017/CCO9781139696456.003

Book Chapters | 2014

Dick J; Pillichshammer F, 2014, 'Discrepancy theory and quasi-Monte Carlo integration', in Lecture Notes in Mathematics, pp. 539 - 619, http://dx.doi.org/10.1007/978-3-319-04696-9_9
Journal articles | 2023

Dick J; Hinrichs A; Novak E; Ritter K; Wasilkowski G; Woźniakowski H, 2023, 'Changes of the Editorial Board', Journal of Complexity, vol. 75, pp. 101728 - 101728, http://dx.doi.org/10.1016/j.jco.2022.101728

Journal articles | 2022

Buratti Y; Dick J; Le Gia Q; Hameiri Z, 2022, 'Deep Learning Extraction of the Temperature-Dependent Parameters of Bulk Defects', ACS Applied Materials and Interfaces, vol. 14, pp. 48647 - 48657, http://dx.doi.org/10.1021/acsami.2c12162

Journal articles | 2022

Dick J; Goda T; Suzuki K, 2022, 'COMPONENT-BY-COMPONENT CONSTRUCTION OF RANDOMIZED RANK-1 LATTICE RULES ACHIEVING ALMOST THE OPTIMAL RANDOMIZED ERROR RATE', MATHEMATICS OF COMPUTATION, http://dx.doi.org/10.1090/mcom/3769

Journal articles | 2022

Dick J; Hinrichs A; Novak E; Ritter K; Wasilkowski G; Woźniakowski H, 2022, 'Changes of the Editorial Board', Journal of Complexity, vol. 68, pp. 101623 - 101623, http://dx.doi.org/10.1016/s0885-064x(21)00078-9

Journal articles | 2022

Dick J; Li G; Tran DD, 2022, 'A new regularization for sparse optimization', ANZIAM Journal, vol. 62, pp. C176 - C191, http://dx.doi.org/10.21914/anziamj.v62.16076

Journal articles | 2022

Dick J; Longo M; Schwab C, 2022, 'Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification', SIAM-ASA Journal on Uncertainty Quantification, vol. 10, pp. 651 - 686, http://dx.doi.org/10.1137/20M1338137

Journal articles | 2022

Le Gia QT; Clarke M; Dick J; Pye D, 2022, 'Elasticity equations with random domains—the shape derivative approach', ANZIAM Journal, vol. 62, pp. C256 - C272, http://dx.doi.org/10.21914/anziamj.v62.16120

Journal articles | 2021

Dick J; Feischl M, 2021, 'A quasi-Monte Carlo data compression algorithm for machine learning', Journal of Complexity, vol. 67, pp. 101587 - 101587, http://dx.doi.org/10.1016/j.jco.2021.101587

Journal articles | 2021

Dick J; Goda T, 2021, 'Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm', Journal of Computational and Applied Mathematics, vol. 382, http://dx.doi.org/10.1016/j.cam.2020.113062

Journal articles | 2021

Dick J; Goda T; Murata H, 2021, 'Toeplitz Monte Carlo', Statistics and Computing, vol. 31, http://dx.doi.org/10.1007/s11222-020-09987-x

Journal articles | 2021

Dick J; Hinrichs A; Novak E; Ritter K; Wasilkowski G; Woźniakowski H, 2021, 'Changes of the Editorial Board', Journal of Complexity, vol. 62, pp. 101533 - 101533, http://dx.doi.org/10.1016/s0885-064x(20)30077-7

Journal articles | 2021

Dick J; Pillichshammer F, 2021, 'Weighted integration over a hyperrectangle based on digital nets and sequences', Journal of Computational and Applied Mathematics, vol. 393, http://dx.doi.org/10.1016/j.cam.2021.113509

Journal articles | 2020

Buratti Y; Le Gia QT; Dick J; Zhu Y; Hameiri Z, 2020, 'Extracting bulk defect parameters in silicon wafers using machine learning models', npj Computational Materials, vol. 6, http://dx.doi.org/10.1038/s41524-020-00410-7

Journal articles | 2020

Dick J; Hinrichs A; Novak E; Ritter K; Sloan I; Wasilkowski G; Woźniakowski H, 2020, 'Editorial board announcements', Journal of Complexity, vol. 59, pp. 101492 - 101492, http://dx.doi.org/10.1016/s0885-064x(20)30035-2

Journal articles | 2020

Dick J; Hinrichs A; Pillichshammer F, 2020, 'A note on the periodic L2 -discrepancy of Korobov’s p-sets', Archiv der Mathematik, vol. 115, pp. 67 - 78, http://dx.doi.org/10.1007/s00013-020-01460-5

Journal articles | 2020

Dick J; Hinrichs A; Pillichshammer F; Prochno J, 2020, 'Tractability properties of the discrepancy in Orlicz norms', Journal of Complexity, vol. 61, http://dx.doi.org/10.1016/j.jco.2020.101468

Journal articles | 2020

Hallett N; Yi K; Dick J; Hodge C; Sutton G; Guang Wang Y; You J, 2020, 'Deep Learning Based Unsupervised and Semi-supervised Classification for Keratoconus', Proceedings of the International Joint Conference on Neural Networks, http://dx.doi.org/10.1109/IJCNN48605.2020.9206694

Journal articles | 2019

Dick J; Feischl M; Schwab C, 2019, 'Improved efficiency of a multi-index fem for computational uncertainty quantification', SIAM Journal on Numerical Analysis, vol. 57, pp. 1744 - 1769, http://dx.doi.org/10.1137/18M1193700

Journal articles | 2019

Dick J; Gantner RN; Le Gia QT; Schwab C, 2019, 'Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion', Computers and Mathematics with Applications, vol. 77, pp. 144 - 172, http://dx.doi.org/10.1016/j.camwa.2018.09.019

Journal articles | 2019

Dick J; Goda T; Yoshiki T, 2019, 'Richardson extrapolation of polynomial lattice rules', SIAM Journal on Numerical Analysis, vol. 57, http://dx.doi.org/10.1137/17M1138601

Journal articles | 2019

Dick J; Rudolf D; Zhu H, 2019, 'A weighted discrepancy bound of quasi-Monte Carlo importance sampling', Statistics and Probability Letters, vol. 149, pp. 100 - 106, http://dx.doi.org/10.1016/j.spl.2019.01.014

Journal articles | 2019

Gunawan D; Tran MN; Suzuki K; Dick J; Kohn R, 2019, 'Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins', Statistics and Computing, vol. 29, pp. 933 - 946, http://dx.doi.org/10.1007/s11222-018-9846-y

Journal articles | 2018

Dick J; Hinrichs A; Novak E; Ritter K; Sloan I; Wasilkowski G; Woźniakowski H, 2018, 'Changes of the Editorial Board', Journal of Complexity, vol. 46, pp. iii - iii, http://dx.doi.org/10.1016/s0885-064x(18)30017-7

Journal articles | 2018

Dick J; Irrgeher C; Leobacher G; Pillichshammer F, 2018, 'On the optimal order of integration in hermite spaces with finite smoothness', SIAM Journal on Numerical Analysis, vol. 56, pp. 684 - 707, http://dx.doi.org/10.1137/16M1087461

Journal articles | 2018

Dick J; Pillichshammer F; Suzuki K; Ullrich M; Yoshiki T, 2018, 'Digital net properties of a polynomial analogue of Frolov's construction', Finite Fields and their Applications, vol. 51, pp. 325 - 350, http://dx.doi.org/10.1016/j.ffa.2018.02.004

Journal articles | 2018

Dick J; Pillichshammer F; Suzuki K; Ullrich M; Yoshiki T, 2018, 'Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices', Annali di Matematica Pura ed Applicata, vol. 197, pp. 109 - 126, http://dx.doi.org/10.1007/s10231-017-0670-3

Journal articles | 2017

Dick J; Gantner RN; Le Gia QT; Schwab C, 2017, 'Multilevel higher-order quasi-Monte Carlo Bayesian estimation', Mathematical Models and Methods in Applied Sciences, vol. 27, pp. 953 - 995, http://dx.doi.org/10.1142/S021820251750021X

Journal articles | 2017

Dick J; Goda T; Suzuki K; Yoshiki T, 2017, 'Construction of interlaced polynomial lattice rules for infinitely differentiable functions', Numerische Mathematik, vol. 137, pp. 257 - 288, http://dx.doi.org/10.1007/s00211-017-0882-x

Journal articles | 2017

Dick J; Gomez-Perez D; Pillichshammer F; Winterhof A, 2017, 'Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration', Proceedings of the American Mathematical Society, vol. 145, pp. 3297 - 3310, http://dx.doi.org/10.1090/proc/13490

Journal articles | 2017

Dick J; Hinrichs A; Markhasin L; Pillichshammer F, 2017, 'DISCREPANCY of SECOND ORDER DIGITAL SEQUENCES in FUNCTION SPACES with DOMINATING MIXED SMOOTHNESS', Mathematika, vol. 63, pp. 863 - 894, http://dx.doi.org/10.1112/S0025579317000213

Journal articles | 2017

Dick J; Hinrichs A; Markhasin L; Pillichshammer F, 2017, 'Optimal Lp-discrepancy bounds for second order digital sequences', Israel Journal of Mathematics, vol. 221, pp. 489 - 510, http://dx.doi.org/10.1007/s11856-017-1555-2

Journal articles | 2017

Zhu H; Dick J, 2017, 'A discrepancy bound for deterministic acceptance-rejection samplers beyond N^{- 1 / 2} in dimension 1', Statistics and Computing, vol. 27, pp. 901 - 911, http://dx.doi.org/10.1007/s11222-016-9661-2

Journal articles | 2016

Dick J; Kritzer P, 2016, 'On a projection-corrected component-by-component construction', Journal of Complexity, vol. 32, pp. 74 - 80, http://dx.doi.org/10.1016/j.jco.2015.08.001

Journal articles | 2016

Dick J; Kuo FY; Le Gia QT; Schwab C, 2016, 'Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations', SIAM Journal on Numerical Analysis, vol. 54, pp. 2541 - 2568, http://dx.doi.org/10.1137/16M1078690

Journal articles | 2016

Dick J; Le Gia QT; Schwab C, 2016, 'Higher order quasi-monte carlo integration for holomorphic, parametric operator equations', SIAM-ASA Journal on Uncertainty Quantification, vol. 4, pp. 48 - 79, http://dx.doi.org/10.1137/140985913

Journal articles | 2016

Dick J; Rudolf D; Zhu H, 2016, 'Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo', Annals of Applied Probability, vol. 26, pp. 3178 - 3205, http://dx.doi.org/10.1214/16-AAP1173

Journal articles | 2015

Aistleitner C; Dick J, 2015, 'Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality', Acta Arithmetica, vol. 167, pp. 143 - 171, http://dx.doi.org/10.4064/aa167-2-4

Journal articles | 2015

Brauchart JS; Dick J; Fang L, 2015, 'Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling', Journal of Computational and Applied Mathematics, vol. 286, pp. 28 - 53, http://dx.doi.org/10.1016/j.cam.2015.02.023

Journal articles | 2015

Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces', Journal of Mathematical Analysis and Applications, vol. 431, pp. 782 - 811, http://dx.doi.org/10.1016/j.jmaa.2015.05.079

Journal articles | 2015

Dick J; Hinrichs A; Pillichshammer F, 2015, 'Proof techniques in quasi-Monte Carlo theory', Journal of Complexity, vol. 31, pp. 327 - 371, http://dx.doi.org/10.1016/j.jco.2014.09.003

Journal articles | 2015

Dick J; Kritzer P; Leobacher G; Pillichshammer F, 2015, 'A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights', Journal of Computational and Applied Mathematics, vol. 276, pp. 1 - 15, http://dx.doi.org/10.1016/j.cam.2014.08.017

Journal articles | 2015

Dick J; Kritzer P; Leobacher G; Pillichshammer F, 2015, 'Numerical integration in log-Korobov and log-cosine spaces', Numerical Algorithms, vol. 70, pp. 753 - 775, http://dx.doi.org/10.1007/s11075-015-9972-y

Journal articles | 2015

Dick J; Kuo FY; Gia QTL; Schwab C, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, vol. 37, pp. A1436 - A1450, http://dx.doi.org/10.1137/151005518

Journal articles | 2015

Dick J; Pillichshammer F, 2015, 'The weighted star discrepancy of Korobov’s p-sets', Proceedings of the American Mathematical Society, vol. 143, pp. 5043 - 5057, http://dx.doi.org/10.1090/proc/12636

Journal articles | 2015

Goda T; Dick J, 2015, 'Construction of Interlaced Scrambled Polynomial Lattice Rules of Arbitrary High Order', Foundations of Computational Mathematics, vol. 15, pp. 1245 - 1278, http://dx.doi.org/10.1007/s10208-014-9226-8

Journal articles | 2014

Aistleitner C; Dick J, 2014, 'Low-discrepancy point sets for non-uniform measures', Acta Arithmetica, vol. 163, pp. 345 - 369, http://dx.doi.org/10.4064/aa163-4-4

Journal articles | 2014

Dick J, 2014, 'Discrepancy bounds for infinite-dimensional order two digital sequences over F2', Journal of Number Theory, vol. 136, pp. 204 - 232, http://dx.doi.org/10.1016/j.jnt.2013.09.012

Journal articles | 2014

Dick J, 2014, 'Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series', Journal of Approximation Theory, vol. 183, pp. 14 - 30, http://dx.doi.org/10.1016/j.jat.2014.03.015

Journal articles | 2014

Dick J; Gnewuch M, 2014, 'Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher-Order Convergence', Foundations of Computational Mathematics, vol. 14, pp. 1027 - 1077, http://dx.doi.org/10.1007/s10208-014-9198-8

Journal articles | 2014

Dick J; Gnewuch M, 2014, 'Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition', Journal of Approximation Theory, vol. 184, pp. 111 - 145, http://dx.doi.org/10.1016/j.jat.2014.04.014

Journal articles | 2014

Dick J; Kritzer P; Pillichshammer F; Woźniakowski H, 2014, 'Approximation of analytic functions in Korobov spaces', Journal of Complexity, vol. 30, pp. 2 - 28, http://dx.doi.org/10.1016/j.jco.2013.05.001

Journal articles | 2014

Dick J; Kuo FY; Le Gia QT; Nuyens D; Schwab C, 2014, 'Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs', SIAM Journal on Numerical Analysis, vol. 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984

Journal articles | 2014

Dick J; Nuyens D; Pillichshammer F, 2014, 'Lattice rules for nonperiodic smooth integrands', Numerische Mathematik, vol. 126, pp. 259 - 291, http://dx.doi.org/10.1007/s00211-013-0566-0

Journal articles | 2014

Dick J; Pillichshammer F, 2014, 'Discrepancy theory and quasi-monte carlo integration', Lecture Notes in Mathematics, vol. 2107, pp. 539 - 619, http://dx.doi.org/10.1007/978-3-319-04696-9__9

Journal articles | 2014

Dick J; Pillichshammer F, 2014, 'Explicit constructions of point sets and sequences with low discrepancy', Explicit constructions of point sets and sequences with low discrepancy, pp. 63 - 86, http://dx.doi.org/10.1515/9783110317930.63

Journal articles | 2014

Dick J; Pillichshammer F, 2014, 'Optimal L2 discrepancy bounds for higher order digital sequences over the finite field F2', Acta Arithmetica, vol. 162, pp. 65 - 99, http://dx.doi.org/10.4064/aa162-1-4

Journal articles | 2014

Dick J; Pillichshammer F, 2014, 'The inverse of the star-discrepancy problem and the generation of pseudo-random numbers', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8865, pp. 173 - 184, http://dx.doi.org/10.1007/978-3-319-12325-7_15

Journal articles | 2014

Dick J; Rudolf D, 2014, 'Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo', Electronic Journal of Probability, vol. 19, http://dx.doi.org/10.1214/EJP.v19-3132

Journal articles | 2014

Owen AB; Dick J; Chen S, 2014, 'Higher order Sobol' indices', Information and Inference, vol. 3, pp. 59 - 81, http://dx.doi.org/10.1093/imaiai/iau001

Journal articles | 2014

Zhu H; Dick J, 2014, 'Discrepancy bounds for deterministic acceptance-rejection samplers', Electronic Journal of Statistics, vol. 8, pp. 678 - 707, http://dx.doi.org/10.1214/14-EJS898

Journal articles | 2013

Brauchart JS; Dick J, 2013, 'A Characterization of Sobolev Spaces on the Sphere and an Extension of Stolarsky’s Invariance Principle to Arbitrary Smoothness', Constructive Approximation, vol. 38, pp. 397 - 445, http://dx.doi.org/10.1007/s00365-013-9217-z

Journal articles | 2013

Brauchart JS; Dick J, 2013, 'A simple proof of Stolarsky's invariance principle', Proceedings of the American Mathematical Society, vol. 141, pp. 2085 - 2096, http://dx.doi.org/10.1090/S0002-9939-2013-11490-5

Journal articles | 2013

Dick J; Kuo FY; Sloan IH, 2013, 'High dimensional numerical integration - the Quasi-Monte Carlo way', Acta Numerica, vol. 22, pp. 133 - 288, http://dx.doi.org/10.1017/S0962492913000044

Journal articles | 2013

Dick J; Matsumoto M, 2013, 'On the fast computation of the weight enumerator polynomial and the t value of digital nets over finite abelian groups', SIAM Journal on Discrete Mathematics, vol. 27, pp. 1335 - 1359, http://dx.doi.org/10.1137/120893677

Journal articles | 2012

Aistleitner C; Brauchart JS; Dick J, 2012, 'Point Sets on the Sphere S^2 with Small Spherical Cap Discrepancy', Discrete and Computational Geometry, vol. 48, pp. 990 - 1024, http://dx.doi.org/10.1007/s00454-012-9451-3

Journal articles | 2012

Baldeaux JF; Dick J; Leobacher G; Nuyens D; Pillichshammer F, 2012, 'Efficient calculation of the worst-case error and (fast) construction component-by-component construction of higher order polynomial lattice rules', Numerical Algorithms, vol. 59, pp. 403 - 431, http://dx.doi.org/10.1007/s11075-011-9497-y

Journal articles | 2012

Brauchart JS; Dick J, 2012, 'Quasi-Monte Carlo rules for numerical integration over the unit sphere S^2', Numerische Mathematik, vol. 121, pp. 473 - 502, http://dx.doi.org/10.1007/s00211-011-0444-6

Journal articles | 2012

Dick J, 2012, 'Random weights, robust lattice rules and the geometry of the cbcrc algorithm', Numerische Mathematik, vol. 122, pp. 443 - 467, http://dx.doi.org/10.1007/s00211-012-0469-5

Journal articles | 2012

Dick J; Kritzer P, 2012, 'A higher order Blokh-Zyablov propagation rule for higher order nets', Finite Fields and Their Applications, vol. 18, pp. 1169 - 1183, http://dx.doi.org/10.1016/j.ffa.2012.08

Journal articles | 2011

Baldeaux JF; Dick J, 2011, 'A construction of polynomial lattice rules with small gain coefficients', Numerische Mathematik, vol. 119, pp. 271 - 297, http://dx.doi.org/10.1007/s00211-011-0385-0

Journal articles | 2011

Baldeaux JF; Dick J; Greslehner J; Pillichshammer F, 2011, 'Construction algorithms for higher order polynomial lattice rules', Journal of Complexity, vol. 27, pp. 281 - 299, http://dx.doi.org/10.1016/j.jco.2010.06.002

Journal articles | 2011

Baldeaux JF; Dick J; Pillichshammer F, 2011, 'Duality theory and propagation rules for higher order nets', Discrete Mathematics, vol. 311, pp. 362 - 386, http://dx.doi.org/10.1016/j.disc.2010.11.002

Journal articles | 2011

Chen S; Dick J; Owen A, 2011, 'Consistency of Markov chain quasi-Monte Carlo on continuous state spaces', Annals of Statistics, vol. 39, pp. 673 - 701, http://dx.doi.org/10.1214/10-AOS831

Journal articles | 2011

Dick J, 2011, 'Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands', Annals of Statistics, vol. 39, pp. 1372 - 1398, http://dx.doi.org/10.1214/11-AOS880

Journal articles | 2011

Dick J, 2011, 'Quasi-Monte Carlo numerical integration on Rs: Digital nets and worst-case error', SIAM Journal on Numerical Analysis, vol. 49, pp. 1161 - 1691, http://dx.doi.org/10.1137/100789853

Journal articles | 2011

Dick J; Larcher G; Pillichshammer F; Woźniakowski H, 2011, 'Exponential convergence and tractability of multivariate integration for Korobov spaces', Mathematics of Computation, vol. 80, pp. 905 - 930, http://dx.doi.org/10.1090/S0025-5718-2010-02433-0

Journal articles | 2010

Baldeaux JF; Dick J; Pillichshammer F, 2010, 'A characterization of higher order nets using Weyl sums and its applications', Uniform Distribution Theory, vol. 5, pp. 133 - 155, http://udt.mat.savba.sk/vol05/no1/91BaDiPi10-1.pdf

Journal articles | 2010

Dick J; Kritzer P, 2010, 'Duality theory and propagation rules for generalized digital nets', Mathematics of Computation, vol. 79, pp. 993 - 1017, http://dx.doi.org/10.1090/S0025-5718-09-02315-1

Journal articles | 2009

Baldeaux JF; Dick J, 2009, 'QMC rules of arbitrary high order: reproducing kernel Hilbert space approach', Constructive Approximation, vol. 30, pp. 495 - 527, http://dx.doi.org/10.1007/s00365-009-9074-y

Journal articles | 2009

Baldeaux JF; Dick J; Kritzer P, 2009, 'On the approximation of smooth functions using generalized digital nets', Journal of Complexity, vol. 25, pp. 244 - 567, http://dx.doi.org/10.1016/j.jco.2009.07.003

Journal articles | 2009

Dick J, 2009, 'The decay of the Walsh coefficients of smooth functions', Bulletin of the Australian Mathematical Society, vol. 80, pp. 430 - 453, http://dx.doi.org/10.1017/S0004972709000392

Journal articles | 2009

Dick J; Niederreiter H, 2009, 'Duality for digital sequences', Journal of Complexity, vol. 25, pp. 406 - 414, http://dx.doi.org/10.1016/j.jco.2009.06.004

Journal articles | 2009

Liu K; Dick J; Hickernell FJ, 2009, 'A multivariate fast discrete Walsh transform with an application to function interpolation', Mathematics of Computation, vol. 78, pp. 1573 - 1591, http://dx.doi.org/10.1090/S0025-5718-09-02202-9

Journal articles | 2008

Dick J, 2008, 'Koksma-Hlawka type inequalities of fractional order', Annali Di Matematica Pura Ed Applicata, vol. 187, pp. 385 - 403, http://dx.doi.org/10.1007/s10231-007-0048-z

Journal articles | 2008

Dick J, 2008, 'Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order', SIAM Journal on Numerical Analysis, vol. 46, pp. 1519 - 1553, http://dx.doi.org/10.1137/060666639

Journal articles | 2008

Dick J; Niederreiter H, 2008, 'On the exact t-value of Niederreiter and Sobol` sequences', Journal of Complexity, vol. 24, pp. 572 - 581, http://dx.doi.org/10.1016/j.jco.2008.05.004

Journal articles | 2008

Dick J; Pillichshammer F; Waterhouse BJ, 2008, 'The construction of good extensible rank-1 lattices', Mathematics of Computation, vol. 77, pp. 2345 - 2373, http://dx.doi.org/10.1090/S0025-5718-08-02009-7

Journal articles | 2008

Hickernell FJ; Dick J, 2008, 'An algorithm-driven approach to error analysis for multidimensional integration', International Journal of Numerical Analysis and Modeling, vol. 5, pp. 167 - 189

Journal articles | 2007

Cristea L; Dick J; Leobacher G; Pillichshammer F, 2007, 'The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets', Numerische Mathematik, vol. 105, pp. 413 - 455, http://dx.doi.org/10.1007/s00211-006-0046-x

Journal articles | 2007

Dick J, 2007, 'A note on the existence of sequences with small star discrepancy', Journal of Complexity, vol. 23, pp. 649 - 652, http://dx.doi.org/10.1016/j.jco.2007.01.004

Journal articles | 2007

Dick J, 2007, 'Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions', SIAM Journal on Numerical Analysis, vol. 45, pp. 2141 - 2176, http://dx.doi.org/10.1137/060658916

Journal articles | 2007

Dick J, 2007, 'The construction of extensible polynomial lattice rules with small weighted star discrepancy', Mathematics of Computation, vol. 76, pp. 2077 - 2085, http://dx.doi.org/10.1090/S0025-5718-07-01984-9

Journal articles | 2007

Dick J; Kritzer P; Kuo FY; Sloan IH, 2007, 'Lattice-Nystrom method for Fredholm integral equations of the second kind with convolution type kernels', Journal of Complexity, vol. 23, pp. 752 - 772, http://dx.doi.org/10.1016/j.jco.2007.03.004

Journal articles | 2007

Dick J; Kritzer P; Leobacher G; Pillichshammer F, 2007, 'Constructions of general polynomial lattice rules based on the weighted star discrepancy', Finite Fields and Their Applications, vol. 13, pp. 1045 - 1070, http://dx.doi.org/10.1016/j.ffa.2006.09.001

Journal articles | 2007

Dick J; Kritzer P; Pillichshammer F; Schmid W, 2007, 'On the existence of higher order polynomial lattices based on a generalized figure of merit', Journal of Complexity, vol. 23, pp. 581 - 593, http://dx.doi.org/10.1016/j.jco.2006.12.003

Journal articles | 2007

Dick J; Leobacher G; Pillichshammer F, 2007, 'Randomized Smolyak algorithms based on digital sequences for multivariate integration', IMA Journal of Numerical Analysis, vol. 27, pp. 655 - 674, http://dx.doi.org/10.1093/imanum/drm002

Journal articles | 2007

Dick J; Leobacher G; Pillichshammer F, 2007, 'Smolyak algorithms based on digital (t,Î±,d)-sequences for multivariate integration', PAMM, vol. 7, pp. 1022403 - 1022404, http://dx.doi.org/10.1002/pamm.200700232

Journal articles | 2007

Dick J; Pillichshammer F, 2007, 'Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules', Journal of Complexity, vol. 27, pp. 436 - 453, http://dx.doi.org/10.1016/j.jco.2007.02.001

Journal articles | 2007

Dick J; Pillichshammer F, 2007, 'Strong tractability of multivariate integration of arbitrary order', PAMM, vol. 7, pp. 1022405 - 1022406, http://dx.doi.org/10.1002/pamm.200700276

Journal articles | 2007

Dick J; Pillichshammer F; Waterhouse BJ, 2007, 'The construction of good extensible Korobov rules', Computing, vol. 79, pp. 79 - 91, http://dx.doi.org/10.1007/s00607-006-0216-9

Journal articles | 2006

Christea LL; Dick J; Pillichshammer F, 2006, 'On the mean square weighted L2 discrepancy of randomized digital nets in prime base', Journal of Complexity, vol. 22, pp. 605 - 629, http://dx.doi.org/10.1016/j.jco.2006.03.005

Journal articles | 2006

Dick J, 2006, 'A Taylor space for multivariate integration', Monte Carlo Methods and Applications, vol. 12, pp. 99 - 111, http://dx.doi.org/10.1163/156939606777488860

Journal articles | 2006

Dick J; Kritzer P, 2006, 'A best possible upper bound on the star discrepancy of (t,m,2)-nets', Monte Carlo Methods and Applications, vol. 12, pp. 1 - 17, http://dx.doi.org/10.1515/156939606776886643

Journal articles | 2006

Dick J; Pillichshammer F, 2006, 'Periodic functions with bounded remainder', Archiv der Mathematik, vol. 87, pp. 554 - 563, http://dx.doi.org/10.1007/s00013-006-1837-0

Journal articles | 2006

Dick J; Sloan IH; Wang XJ; Wozniakowski H, 2006, 'Good lattice rules in weighted Korobov spaces with general weights', Numerische Mathematik, vol. 103, pp. 63 - 97, http://dx.doi.org/10.1007/s00211-005-0674-6

Journal articles | 2006

Pirsic G; Dick J; Pillichshammer F, 2006, 'Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces', SIAM Journal on Numerical Analysis, vol. 44, pp. 385 - 411, http://dx.doi.org/10.1137/050622638

Journal articles | 2005

Dick J; Kritzer P, 2005, 'Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2)-sequences over Z(2)', ACTA Mathematica Hungarica, vol. 109, pp. 239 - 254, http://dx.doi.org/10.1007/s10474-005-0243-6

Journal articles | 2005

Dick J; Kuo FY; Pillichshammer F; Sloan IH, 2005, 'Construction algorithms for polynomial lattice rules for multivariate integration', Mathematics of Computation, vol. 74, pp. 1895 - 1921, http://dx.doi.org/10.1090/S0025-5718-05-01742-4

Journal articles | 2005

Dick J; Leobacher G; Pillichshammer F, 2005, 'Construction algorithms for digital nets with low weighted star discrepancy', SIAM Journal on Numerical Analysis, vol. 43, pp. 76 - 95, http://dx.doi.org/10.1137/040604662

Journal articles | 2005

Dick J; Pillichshammer F, 2005, 'A note on the figure of merit of 2-dimensional rank 2 lattice rules', Integers: the Electronic Journal of Combinatorial Number Theory, vol. 5, pp. #A05

Journal articles | 2005

Dick J; Pillichshammer F, 2005, 'Diaphony, discrepancy, spectral test and worst-case error', Mathematics and Computers in Simulation, vol. 70, pp. 159 - 171, http://dx.doi.org/10.1016/j.matcom.2005.06.004

Journal articles | 2005

Dick J; Pillichshammer F, 2005, 'Dyadic diaphony of digital nets over Z(2)', Monatshefte fur Mathematik, vol. 145, pp. 285 - 299, http://dx.doi.org/10.1007/s00605-004-0287-7

Journal articles | 2005

Dick J; Pillichshammer F, 2005, 'Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces', Journal of Complexity, vol. 21, pp. 149 - 195, http://dx.doi.org/10.1016/j.jco.2004.07.003

Journal articles | 2005

Dick J; Pillichshammer F, 2005, 'On the mean square weighted L_2 discrepancy of randomized digital (t,m,s)-nets over Z_2', ACTA Arithmetica, vol. 117, pp. 371 - 403, http://dx.doi.org/10.4064/aa117-4-4

Journal articles | 2004

Dick J, 2004, 'On the convergence rate of the component-by-component construction ofgood lattice rules', Journal of Complexity, vol. 20, pp. 493 - 522, http://dx.doi.org/10.1016/j.jco.2003.11.008

Journal articles | 2004

Dick J; Kuo FY, 2004, 'Reducing the construction cost of the component-by-component construction of good lattice rules', Mathematics of Computation, vol. 73, pp. 1967 - 1988, http://dx.doi.org/10.1090/S0025-5718-03-01610-7

Journal articles | 2004

Dick J; Sloan IH; Wang XJ; Wozniakowski H, 2004, 'Liberating the weights', Journal of Complexity, vol. 20, pp. 593 - 623, http://dx.doi.org/10.1016/j.jco.2003.06.002

Journal articles | 2004

Wang X; Sloan IH; Dick J, 2004, 'On Korobov lattice rules in weighted spaces', SIAM Journal on Numerical Analysis, vol. 42, pp. 1760 - 1779, http://dx.doi.org/10.1137/S0036142903425021
Preprints | 2020

Dick J; Hinrichs A; Pillichshammer F, 2020, A note on the periodic $L_2$-discrepancy of Korobov's $p$-sets, http://dx.doi.org/10.48550/arxiv.2001.01973

Preprints | 2020

Hallett N; Yi K; Dick J; Hodge C; Sutton G; Wang YG; You J, 2020, Deep Learning Based Unsupervised and Semi-supervised Classification for Keratoconus, http://dx.doi.org/10.48550/arxiv.2001.11653

Conference Papers | 2019

Buratti Y; Dick J; Le Gia Q; Hameiri Z, 2019, 'A machine learning approach to defect parameters extraction: Using random forests to inverse the shockley-read-hall equation', Chicago, USA, presented at 46th IEEE photovoltaic specialists conference, Chicago, USA, 17 June 2019 - 21 June 2019

Conference Papers | 2019

Buratti Y; Dick J; Le Gia Q; Zhu Y; Hameiri Z, 2019, 'Inversion of the Shockley-Read-Hall equation using random forests', Canberra, presented at Asia Pacific Solar Research Conference, Canberra, 03 December 2019

Preprints | 2019

Dick J; Hinrichs A; Pillichshammer F; Prochno J, 2019, Tractability properties of the discrepancy in Orlicz norms, http://dx.doi.org/10.48550/arxiv.1910.12571

Preprints | 2017

Dick J; Pillichshammer F; Suzuki K; Ullrich M; Yoshiki T, 2017, Digital net properties of a polynomial analogue of Frolov's construction, http://dx.doi.org/10.48550/arxiv.1712.06831

Preprints | 2016

Dick J; Gantner RN; Gia QTL; Schwab C, 2016, Higher order Quasi-Monte Carlo integration for Bayesian Estimation, http://dx.doi.org/10.48550/arxiv.1602.07363

Preprints | 2016

Dick J; Gantner RN; Gia QTL; Schwab C, 2016, Multilevel higher order Quasi-Monte Carlo Bayesian Estimation, http://dx.doi.org/10.48550/arxiv.1611.08324

Preprints | 2016

Dick J; Hinrichs A; Markhasin L; Pillichshammer F, 2016, Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness, http://dx.doi.org/10.48550/arxiv.1604.08713

Preprints | 2016

Dick J; Hinrichs A; Markhasin L; Pillichshammer F, 2016, Optimal $L_p$-discrepancy bounds for second order digital sequences, http://dx.doi.org/10.48550/arxiv.1601.07281

Preprints | 2016

Dick J; Irrgeher C; Leobacher G; Pillichshammer F, 2016, On the optimal order of integration in Hermite spaces with finite smoothness, http://dx.doi.org/10.48550/arxiv.1608.06061

Preprints | 2016

Dick J; Pillichshammer F; Suzuki K; Ullrich M; Yoshiki T, 2016, Lattice based integration algorithms: Kronecker sequences and rank-1 lattices, http://dx.doi.org/10.48550/arxiv.1608.08687

Conference Papers | 2016

Zhu H; Dick J, 2016, 'Discrepancy estimates for acceptance-rejection samplers using stratified inputs', in Springer Proceedings in Mathematics and Statistics, pp. 599 - 619, http://dx.doi.org/10.1007/978-3-319-33507-0_33

Preprints | 2015

Dick J; Gomez-Perez D; Pillichshammer F; Winterhof A, 2015, Digital inversive vectors can achieve strong polynomial tractability for the weighted star discrepancy and for multivariate integration, http://dx.doi.org/10.48550/arxiv.1512.06521

Preprints | 2015

Dick J; Kuo FY; Gia QTL; Schwab C, 2015, Fast QMC matrix-vector multiplication, http://dx.doi.org/10.48550/arxiv.1501.06286

Preprints | 2014

Brauchart JS; Dick J; Fang L, 2014, Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling, http://dx.doi.org/10.48550/arxiv.1408.4609

Preprints | 2014

Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2014, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, http://dx.doi.org/10.48550/arxiv.1407.8311

Preprints | 2014

Dick J; Gia QTL; Schwab C, 2014, Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification, http://dx.doi.org/10.48550/arxiv.1409.7970

Preprints | 2014

Dick J; Gia QTL; Schwab C, 2014, Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations, http://dx.doi.org/10.48550/arxiv.1409.2180

Preprints | 2014

Dick J; Hinrichs A; Pillichshammer F, 2014, Proof Techniques in Quasi-Monte Carlo Theory, http://dx.doi.org/10.48550/arxiv.1403.7334

Preprints | 2014

Dick J; Kritzer P; Leobacher G; Pillichshammer F, 2014, A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights, http://dx.doi.org/10.48550/arxiv.1404.5497

Preprints | 2014

Dick J; Kritzer P; Leobacher G; Pillichshammer F, 2014, Numerical integration in $\log$-Korobov and $\log$-cosine spaces, http://dx.doi.org/10.48550/arxiv.1411.2715

Preprints | 2014

Dick J; Kuo F; Gia QTL; Schwab C, 2014, Multi-level higher order QMC Galerkin discretization for affine parametric operator equations, http://dx.doi.org/10.48550/arxiv.1406.4432

Conference Papers | 2014

Dick J; Le Gia QT; Schwab CH, 2014, 'Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification', in Kirby RM; Berzins M; Hesthaven JS (eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Salt Lake City, Utah, USA, pp. 445 - 453, presented at ICOSAHOM conference, Salt Lake City, Utah, USA, 23 June 2014 - 27 June 2014, http://dx.doi.org/10.1007/978-3-319-19800-2_41

Conference Proceedings (Editor of) | 2013

2013, 'Monte Carlo and Quasi-Monte Carlo Methods 2012', Springer Science & Business Media, Vol. 65, http://dx.doi.org/10.1007/978-3-642-41095-6

Preprints | 2013

Dick J; Kuo FY; Gia QTL; Nuyens D; Schwab C, 2013, Higher order QMC Galerkin discretization for parametric operator equations, http://dx.doi.org/10.48550/arxiv.1309.4624

Conference Papers | 2013

Dick J; Kuo FY; Peters GW; Sloan IH, 2013, 'Preface', in Springer Proceedings in Mathematics and Statistics

Other | 2012

Dick J, 2012, A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules, http://arxiv.org/abs/1207.5275v1

Preprints | 2012

Dick J; Kritzer P; Pillichshammer F; Woźniakowski H, 2012, Approximation of analytic functions in Korobov spaces, http://dx.doi.org/10.48550/arxiv.1211.5822

Preprints | 2012

Dick J; Nuyens D; Pillichshammer F, 2012, Lattice rules for nonperiodic smooth integrands, http://dx.doi.org/10.48550/arxiv.1211.3799

Preprints | 2011

Aistleitner C; Brauchart J; Dick J, 2011, Point sets on the sphere $\mathbb{S}^2$ with small spherical cap discrepancy, http://dx.doi.org/10.48550/arxiv.1109.3265

Preprints | 2011

Baldeaux J; Dick J; Leobacher G; Nuyens D; Pillichshammer F, 2011, Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules, http://dx.doi.org/10.48550/arxiv.1105.2599

Preprints | 2011

Brauchart JS; Dick J, 2011, A simple Proof of Stolarsky's Invariance Principle, http://dx.doi.org/10.48550/arxiv.1101.4448

Preprints | 2011

Brauchart JS; Dick J, 2011, Quasi-Monte Carlo rules for numerical integration over the unit sphere $\mathbb{S}^2$, http://dx.doi.org/10.48550/arxiv.1101.5450

Preprints | 2010

Baldeaux J; Dick J, 2010, A Construction of Polynomial Lattice Rules with Small Gain Coefficients, http://dx.doi.org/10.48550/arxiv.1003.4785

Conference Papers | 2008

Dick J, 2008, 'On quasi-Monte Carlo rules achieving higher order convergence', in Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, New York, pp. 73 - 96, presented at Monte Carlo and Quasi-Monte Carlo Methods 2008, Montreal, Canada, 06 July 2008 - 11 July 2008, http://dx.doi.org/10.1007/978-3-642-04107-5-5

Conference Papers | 2008

Dick J; Baldeaux JF, 2008, 'Equidistribution properties of generalized nets and sequences', in Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, New York, pp. 305 - 322, presented at Monte Carlo and Quasi-Monte Carlo Methods 2008, Montreal, Canada, 06 July 2008 - 11 July 2008, http://dx.doi.org/10.1007/978-3-642-04107-5-19

Conference Papers | 2006

Dick J; Kritzer P; Kuo FY, 2006, 'Approximation of functions using digital nets', in 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, pp. 275 - 297, presented at 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, 14 August 2006 - 18 August 2006

Conference Papers | 2004

Dick J; Niederreiter H; Pillichshammer F, 2004, 'Weighted Star Discrepancy of Digital Nets in Prime Bases', in Niederreiter H; Talay D (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, SPRINGER-VERLAG BERLIN, France, pp. 77 - +, presented at Monte Carlo and Quasi-Monte Carlo Methods 2004, France, 07 June 2004 - 10 June 2004, http://dx.doi.org/10.1007/3-540-31186-6_6

Conference Papers | 2002

Dick J; Kuo FY, 2002, 'Constructing good lattice rules with millions of points', in Niederreiter H (ed.), 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), SPRINGER-VERLAG BERLIN, National University of Singapore, pp. 181 - 197, presented at 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), National University of Singapore, 25 November 2002 - 28 November 2002, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000189463200010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a

Follow