Editorial Duties
Awards
Students
PhD
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Jan Baldeaux, Higher order nets and sequences, 2007-2010 (co-supervisor).
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Houying Zhu, Markov chain quasi-Monte Carlo methods, August 2012 to March 2016 (main supervisor).
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Yi-Lung Chen, February 2017 to present (co-supervisor).
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Dinh Duy Tran, February 2019 to present (main supervisor).
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Yoann Buratti, June 2019 to present (co-supervisor).
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Xiongwen Ke, June 2019 to present (co-supervisor).
Honours students
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Dinh Duy Tran, A Bayesian approach for inverse problems in uncertainty quantification. Honours in Applied Mathematics, 2018.
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Michael Wang, Computational methods for sovling PDEs with random coefficients. Honours in Statistics, 2018.
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Allan Loi, Constructive approximations with Neural Networks. Honours in Applied Mathematics, 2018. Awarded University Medal.
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Haohao Chen, Constructing well distributed points using clustering. Honours in Applied Mathematics, 2020.
Masters students
- Quan Zhang, Fast QMC matrix vector multiplication in pricing financial options. Masters in Financial Mathematics. Semester 1, 2016.
- Xuebin Zheng, Pseudo-marginal Metropolis-Hastings approach and its application to Bayesian copula models. Masters in Financial Mathematics. Semester 2, 2016.
- Guobin Wang, Deterministic Acceptance-Rejection sampling. Master in Financial Mathematics, Semester 2, 2017.
- Siting Li, Multilevel Monte Carlo Method. Masters in Statistics, Semester 1, 2018.
- Qiyue Liu, Monte Carlo and quasi-Monte Carlo simulation to price various options. Master in Financial Mathematics, Semester 1, 2018.
- Xiongwen Ke, Learning with imbalanced data. Master in Financial Mathematics. Semester 1, 2018.
- Zhengyue Gu, Machine learning methods to forecast PM2.5 concentrations: A case study in Taiwan. Masters in Statistics, Semester 2, 2018.
- Mengfei Lu, The momentum effect and the binomial option pricing model. Master in Statistics, Term 1 and 2, 2019.
- Ho Wah Chan, Statistical analysis of the housing market. Master in Statistics, Term 1 and 2, 2019.
- Hasan Salloukh, Modeling financial data using Garch models. Master in Financial Mathematics, Term 1 and 2, 2019.
- Manoj Kumar Palani, A Monte Carlo tree search component-by-component construction of lattice rules. Master in Mathematics, Term 1 and 2, 2020.
- Ho Man Chan, Volatility forecasting using Garch model and implied volatility. Master in Financial Mathematics, Term 1 and 2, 2020
- My Bui, The Dupiree model in option pricing. Master in Financial Mathematics, Term 1 and 2, 2021.
- Zhuo Wang, The regime switching model in option pricing, Term 1 and 2, 2021.
- Ziming Wang, Term 2 and 3, 2021.
- Ge Wang, Term 2 and 3, 2021.
Projects for PhD, honours or master students
For some possible projects in Statistics, Computational Mathematics or Number Theory click
here. Information on Scholarships for Australian and international students can be found at the
UNSW Graduate Research School page.
Grants
- Chief investigator for a Discovery Project from the Australian Research Council, AUD 315K over 3 years (2019--2021) for the project ''Novel mathematics and numerical methods for ferromagnetic problems'', DP190101197. Chief Investigator (CI) A/Prof. Thanh Tran (UNSW), CI A/Prof. Josef Dick (UNSW), Partner Investigator (PI) Dr. Michael Feischl (Vienna University of Technology), PI Prof. Dirk Praetorius (Vienna University of Technology), PI Prof. Andreas Prohl (Eberhard Karls University of Tuebingen).
- Chief investigator for Discovery Project from the Australian Research Council, AUD 375,100 over 3 years (2015-2017) for the project ``Quantifying uncertainty: Innovations in high dimensional computation'', DP150101770. Chief Investigator (CI) A/Prof. Josef Dick (UNSW), CI Dr. Frances Y. Kuo (UNSW), CI Prof. Ian Sloan (UNSW), Partner Investigator (PI) Prof. Michael Giles (University of Oxford), PI Prof. Michael Griebel (University of Bonn).
- Chief investigator for Discovery project from the Australian Research Council, AUD 500,000 over 3 years (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, AUD 735,000 over 5 years (2010-2014) for the project ``Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo''.
- UNSW Vice Chancellor Fellowship 2006 - 2009.
Matlab programs
- Higher order QMC: A Matlab function to generate interlaced Sobol points can be found here.
- Randomized higher order QMC: A Matlab function to generate scrambled interlaced Sobol points can be found here.
- Fast QMC matrix-vector multiplication: Non-optimized implementations in Matlab together with some examples can be found here.
There are a number of online resources for generating QMC point sets. The
magic point shop from Dirk Nuyens contains programs to do the component-by-component construction and to generate the points. The
Tools for Higher-Order Quasi-Monte Carlo website from Robert N. Gantner at SAM ETH Zürich, has point sets for generating higher-order Quasi-Monte Carlo rules, with a focus on interlaced polynomial lattice rules. Ísabel Piršić has generating matrices for
Niederreiter-Xing nets. Frances Y. Kuo has
lattice rule generating vectors and
Sobol sequence generators.
MCQMC Wiki
The
Monte Carlo and quasi-Monte Carlo (MCQMC) Wiki page contains a lot of free online material.
arXiv
Many of my preprints can be found on
my arXiv page.
List of publications
Josef Dick's publication listed in MathSciNet can be found
here and his MathSciNet profile
here.
Book
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J. Dick and F. Pillichshammer, Digital Nets and Sequences. Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, Cambridge, 2010, 600 pages.
ISBN 978-0-521-19159-3. © Cambridge University Press. The book can be ordered from Cambridge University Press here. For a list of known misprints see here. For a preprint version see here. Note that the preprint version differs from the published book. In particular, the page numbers are different. However, numbers of Chapters, Sections, Theorems, Lemmas, Corollaries, Definitions and Examples are the same. Answers to selected exercises can be found here.
Editorial Work
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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 held at the University of New South Wales, Sydney, Australia, February 13-17, 2012. Edited by Josef Dick, Frances Y. Kuo, Gareth W. Peters, and Ian H. Sloan. Springer-Verlag, 2014.
The monograph can be purchased from Springer here. A preprint version is available here.
Accepted manuscripts
- J. Dick and M. Feischl, A quasi-Monte Carlo data compression algorithm for machine learning. Accepted for publication in J. Complexity, 28 May, 2021.
Appeared 2021
- J. Dick, T. Goda, Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm. J. Comput. Appl. Math., 382, 113062, 2021.
- J. Dick, T. Goda, H. Murata, Toeplitz Monte Carlo. Stat. Comput., 31, 1, 2021.
Appeared 2020
- Y. Buratti, Q. T. Le Gia, J. Dick, Y. Zhu, Z. Hameiri, Extracting Bulk Defect Parameters in Silicon Wafers using Machine Learning Models. npj Computational Materials, 6, 142, 2020.
- J. Dick, A. Hinrichs, F. Pillichshammer, A note on the periodic $L_2$-discrepancy of Korobov's $p$-sets. Arch. Math. (Basel), 115, 1, 67--78, 2020.
- J. Dick, A. Hinrichs, F. Pillichshammer, J. Prochno, Tractability properties of the discrepancy in Orlicz norms. J. Complexity, 61, 101468, p. 9, 2020.
- N.~Hallett, K.~Yi, J.~Dick, Ch.~Hodge, G.~Sutton, Y.G.~Wang, J.J.~You, Deep learning based unsupervised and semi-supervised classification for corneal disease diagnosis. In International Joint Conference in Neural Networks (IJCNN) Proceedings 2020.
Appeared 2019
- J. Dick, M. Feischl, and Ch. Schwab, Improved efficiency of a multi-index FEM for computational uncertainty quantification. SIAM J. Numer. Anal., 57, 1744--1769, 2019.
- J. Dick, R. N. Gantner, Quoc T. Le Gia, and Ch. Schwab, Higher order Quasi-Monte Carlo integration for Bayesian estimation. Computers and Mathematics with Applications, 77, 144--172, 2019.
- J. Dick, T. Goda, and T. Yoshiki, Richardson extrapolation of polynomial lattice rules. SIAM J. Numer. Anal., 57, 44--69, 2019.
- J. Dick, D. Rudolf, H. Zhu, A weighted Discrepancy Bound of quasi-Monte Carlo Importance sampling. Statist. Probab. Lett., 149, 100--106, 2019.
- D. Gunawan, M.-N. Tran, K. Suzuki, J. Dick, and R. Kohn, Computationally Efficient Bayesian Estimation of High Dimensional Copulas with Discrete and Mixed Margins. Statistics and Computing, 29, 933--946, 2019.
Appeared 2018
- J. Dick, Ch. Irrgeher, G. Leobacher, and F. Pillichshammer, On the optimal order of integration in Hermite spaces with finite smoothness. SIAM J. Numer. Anal., 56, 684--707, 2018.
- J. Dick, F. Pillichshammer, K. Suzuki, M. Ullrich, T. Yoshiki, Digital net properties of a polynomial analogue of Frolov's construction. Finite Fields and their Applications, 51, 325--350, 2018.
- J. Dick, F. Pillichshammer, K. Suzuki, M. Ullrich, and T. Yoshiki, Lattice based integration algorithms: Kronecker sequences and rank-1 lattices. Annali di Mat et Pura et Appl., 197, 109--126, 2018.
Appeared 2017
- J. Dick, R. N. Gantner, Quoc T. Le Gia, and Ch. Schwab, Multi-level higher order quasi-Monte Carlo Bayesian estimation. Math. Models Methods Appl. Sci., 27, 953--995, 2017.
- J. Dick, T. Goda, K. Suzuki, and T. Yoshiki, Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Numer. Math., 137, 257--288, 2017. For the arXiv version see here.
- J. Dick, D. Gomez-Perez, F. Pillichshammer, and A. Winterhof, Digital inversive vectors can achieve strong polynomial tractability for the weighted star discrepancy and for multivariate integration. Proc. Amer. Math. Soc., 145, 3297--3310, 2017. For the arXiv version see here.
- J. Dick, A. Hinrichs, L. Markhasin, and F. Pillichshammer, Optimal $L_p$-discrepancy bounds for second order digital sequences. Israel J. Math., 221, 489--510, 2017. For the arXiv version see here.
- J. Dick, A. Hinrichs, L. Markhasin, and F. Pillichshammer, Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Mathematika, 63, 863--894, 2017.
- H. Zhu and J. Dick, Discrepancy bound for deterministic acceptance-rejection sampler beyond $N^{-1/2}$ in dimension $1$. Stat. Comput., 27, 901--911, 2017. For the arXiv version see here.
Appeared 2016
- J. Dick and P. Kritzer, On a projection-corrected component-by-component construction. J. Complexity, 32, 74--80, 2016. DOI: 10.1016/j.jco.2015.08.001 For the arXiv version see here.
- J. Dick, F. Y. Kuo, Q. T. Le Gia, and Ch. Schwab, Multi-level higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. SIAM J. Numer. Anal., 54, 2541--2568, 2016. For the arXiv version see here.
- J. Dick, Q. T. Le Gia and Ch. Schwab, Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations. SIAM/ASA J. Uncert. Quant., 4, 48--79, 2016. For the arXiv version see here.
- J. Dick, D. Rudolf and H. Zhu, Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. Ann. Appl. Probab., 26, 3178--3205, 2016. For the arXiv version see here.
- H. Zhu and J. Dick, Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs. In R. Cools and D. Nuyens (eds.), Monte Carlo and Quasi-Monte Carlo Methods, Springer Verlag, Switzerland, 2016, pp. 599--619. For the arXiv version see here.
Appeared 2015
- Ch. Aistleitner and J. Dick, Functions of bounded variation, signed measures, and a general Koksma--Hlawka inequality. Acta Arith., 167, 143--171, 2015. DOI: 10.4064/aa167-2-4 For the arXiv version see here.
- J. S. Brauchart, J. Dick and L. Fang, Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. J. Comput. Appl. Math., 286, 28--53, 2015. DOI: 10.1016/j.cam.2015.02.023 For the arXiv version see here.
- J. S. Brauchart, J. Dick, E. B. Saff, I. H. Sloan, YG. Wang and R. S. Womersley, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. J. Math. Anal. Appl., 431, 782--811, 2015. DOI: 10.1016/j.jmaa.2015.05.079 For the arXiv version see here.
- J. Dick, A. Hinrichs and F. Pillichshammer, Proof techniques in Quasi-Monte Carlo theory. J. Complexity, 31, 327--371, 2015. DOI: 10.1016/j.jco.2014.09.003 For the arXiv version see here.
- J. Dick, P. Kritzer, G. Leobacher and F. Pillichshammer, A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. J. Comp. Appl. Math., 276, 1--15, 2015. DOI: 10.1016/j.cam.2014.08.017 For the arXiv version see here.
- J. Dick, P. Kritzer, G. Leobacher and F. Pillichshammer, Numerical integration in log-Korobov and log-cosine spaces. Numer. Alg., 70, 753--775, 2015. DOI: 10.1016/10.1007/s11075-015-9972-y For the arXiv version see here.
- J. Dick, Q. T. Le Gia, F. Y. Kuo and Ch. Schwab, Fast QMC matrix-vector multiplication. SIAM J. Sci. Comput., 37, A1436--A1450, 2015. DOI: 10.1137/151005518 For the arXiv version see here. Non-optimized implementations of the fast QMC matrix-vector multiplication in Matlab together with some examples can be found here.
- J. Dick, Q. T. Le Gia and Ch. Schwab, Higher order Quasi-Monte Carlo integration in uncertainty quantification. In: R. M. Kirby, M. Berzins and J. S. Hesthaven, (eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Springer, pp. 445--453, 2015. For the arXiv version see here.
- J. Dick and F. Pillichshammer, The weighted star discrepancy of Korobov's p-sets. Proc. Amer. Math. Soc., 143, 5043--5057, 2015. DOI: 10.1090/proc/12636 For the arXiv version see here.
- T. Goda and J. Dick, Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Found. Comput. Math., 15, 1245--1278, 2015. DOI: 10.1007/s10208-014-9226-8 For the arXiv version see here.
Appeared 2014
- Ch. Aistleitner and J. Dick, Low-discrepancy point sets for non-uniform measures. Acta Arith., 163, 345--369, 2014. DOI: 10.4064/aa163-4-4 For the arXiv version see here.
- J. Dick, Discrepancy bounds for infinite-dimensional order two digital sequences over F_2. J. Number Th., 136, 204--232, 2014. DOI:10.1016/j.jnt.2013.09.012 For the arXiv version see here.
- J. Dick, Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine-, and Walsh series. J. Approx. Theory, 183, 14--30, 2014. DOI: 10.1016/j.jat.2014.03.015 For the arXiv version see here.
- J. Dick, Applications of geometric discrepancy in numerical analysis and statistics. In: Larcher G., Pillichshammer F., Winterhof A., and Xing C.P. (eds.), Applied Algebra and Number Theory. Cambridge University Press, Cambridge, 2014, pp. 39--57. For the arXiv version see here.
- J. Dick and M. Gnewuch, Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. J. Approx. Theory, 184, 111--145, 2014. DOI: 10.1016/j.jat.2014.04.014 For the arXiv version see here.
- J. Dick and M. Gnewuch, Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher Order Convergence. DOI: 10.1007/s10208-014-9198-8 Found. Comput. Math., 14, 1027--1077, 2014. For the arXiv version see here.
- J. Dick, P. Kritzer, F. Pillichshammer, H. Wozniakowski, Approximation of analytic functions in Korobov spaces. J. Complexity, 30, 2--28, 2014. DOI:10.1016/j.jco.2013.05.001 For the arXiv version see here.
- J. Dick, F. Y. Kuo, Q. T. Le Gia, D. Nuyens and Ch. Schwab, Higher order QMC Galerkin discretization for parametric operator equations. SIAM J. Numer. Anal., 52, 2676--2702, 2015. DOI:10.1137/130943984 For the arXiv version see here.
- J. Dick, D. Nuyens and F. Pillichshammer, Lattice rules for nonperiodic smooth integrands. Numer. Math., 126, 259--291, 2013. DOI: 10.1007/s00211-013-0566-0 For the arXiv version see here.
- J. Dick and F. Pillichshammer, Optimal L_2 discrepancy bounds for higher order digital sequences over the finite field F_2. Acta Arith., 162, 65--99, 2014. DOI:10.4064/aa162-1-4 For the arXiv version see here.
- J. Dick and F. Pillichshammer, Explicit constructions of point sets and sequences with low discrepancy. In: P. Kritzer, H. Niederreiter, F. Pillichshammer and A. Winterhof (eds.), Uniform Distribution and Quasi-Monte Carlo Methods. Discrepancy, Integration and Applications, De Gruyter, Berlin, 2014, pp. 63--86. For the arXiv version see here.
- J. Dick and F. Pillichshammer, The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. In: K.-U. Schmidt and A. Winterhof (eds.), Sequences and their Applications -- SETA 2014, Springer, Lecture Notes in Computer Science 8865, Heidelberg, 2014, pp. 173--184. For the arXiv version see here.
- J. Dick and F. Pillichshammer, Discrepancy theory and quasi-Monte Carlo integration. In: W. W. L. Chen, A. Srivastav, G. Travaglini (eds.), Panoramy in Discrepancy Theory, Springer Verlag, Cham, 2014, pp. 539--619. See here for a preprint version.
- J. Dick and D. Rudolf, Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo. Electron. J. Probab., 19, 1--24, 2014. DOI:10.1214/EJP.v19-3132 For the arXiv version see here.
- A. Owen, J. Dick and S. Chen, Higher order Sobol' indices. Information and Inference, 3, 59--81, 2014. DOI:10.1093/imaiai/iau001 For the arXiv version see here. The published version can be downloaded free of charge here.
- H. Zhu and J. Dick, Discrepancy bounds for deterministic acceptance-rejection samplers. Electron. J. Stat., 8, 678--707, 2014. DOI:10.1214/14-EJS898 For the arXiv version see here.
Appeared 2013
- J. S. Brauchart and J. Dick, A simple proof of Stolarsky's invariance principle. Proc. Amer. Math. Soc., 141, 2085--2096, 2013. DOI:10.1090/S0002-9939-2013-11490-5 For the arXiv version see here.
- J. Brauchart and J. Dick, A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness. Constr. Approx., 38, 397--445, 2013. DOI:10.1007/s00365-013-9217-z For the arXiv version see here.
- J. Dick, F. Y. Kuo and I. H. Sloan, High dimensional numerical integration - the Quasi-Monte Carlo way. Acta Numerica, 22, 133--288, 2013. DOI: 10.1017/S09624929130 The published paper can be downloaded from the publishers website here. It can also be freely downloaded from here.
- J. Dick and M. Matsumoto, On the fast computation of the weight enumerator polynomial and the t value of digital nets over finite abelian groups. SIAM J. Discrete Math., 27, 1335--1359, 2013. DOI:10.1137/120893677 For the arXiv version see here.
Appeared 2012
- Ch. Aistleitner, J. Brauchart and J. Dick, Point sets on the sphere S^2 with small spherical cap discrepancy. Discrete Comput. Geom., 48, 990--1024, 2012. DOI: 10.1007/s00454-012-9451-3 For an arXiv version see here.
- J. Baldeaux, J. Dick, G. Leobacher, D. Nuyens and F. Pillichshammer, Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Numer. Alg., 59, 403--431, 2012. DOI: 10.1007/s11075-011-9497-y For an arXiv version see here.
- J. S. Brauchart and J. Dick, Quasi-Monte Carlo rules for numerical integration over the unit sphere S. Numer. Math., 121, 473--502, 2012. DOI: 10.1007/s00211-011-0444-6 For an arXiv version see here.
- J. Dick, Random weights, robust lattice rules and the geometry of the cbcrc algorithm. Numer. Math., 122, 443--467, 2012. DOI: 10.1007/s00211-012-0469-5 For an arXiv version see here.
- J. Dick and P. Kritzer, A higher order Blokh-Zyablov propagation rule for higher order nets. Finite Fields App., 18, 1169--1183, 2012. DOI: 10.1016/j.ffa.2012.08.003 For an arXiv version see here.
Appeared 2011
- J. Baldeaux and J. Dick, A Construction of Polynomial Lattice Rules with Small Gain Coefficients. Numer. Math., 119, 271--297, 2011. doi:10.1007/s00211-011-0385-0 For a blog entry and a preprint version of this paper see here.
- J. Baldeaux, J. Dick, J. Greslehner, and F. Pillichshammer, Construction algorithms for higher order polynomial lattice rules. J. Complexity, 27, 281--299, 2011.doi:10.1016/j.jco.2010.06.002
- J. Baldeaux, J. Dick, and F. Pillichshammer, Duality Theory and Propagation Rules for Higher Order Nets. Discrete Math., 311, 362--386, 2011. doi:10.1016/j.disc.2010.11.002 For a blog entry and a preprint version of this paper see here.
- S. Chen, J. Dick and A.B. Owen, Consistency of Markov Chain Quasi-Monte Carlo on continuous state spaces. Ann. Stat., 39, 679--701, 2011. doi: 10.1214/10-AOS831 For a blog entry and preprint version of this paper see here.
- J. Dick, Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands. Ann. Stat., 39, 1372--1398, 2011. doi: 10.1214/11-AOS880 For a blog entry and preprint version of this paper see here.
- J. Dick, Quasi-Monte Carlo integration on $\mathbb{R}^s$: digital nets and worst-case error. SIAM J. Numer. Anal., 49, 1661--1691, 2011. doi: 10.1137/100789853 For a blog entry and preprint version of this paper see here and also here.
- J. Dick, G. Larcher, F. Pillichshammer, and H. Wozniakowski, Exponential Convergence and Tractability of Multivariate Integration for Korobov Spaces. Math. Comp., 80, 905--930, 2011. doi: 10.1090/S0025-5718-2010-02433-0 For a blog entry and preprint version of this paper see here.
Appeared 2010
- J. Baldeaux, J. Dick, and F. Pillichshammer, A characterization of higher order nets using Weyl sums and its applications. Uniform Distr. Theory, 5, 133--155, 2010.
- J. Dick and P. Kritzer, Duality theory and propagation rules for generalized digital nets. Math. Comp., 79, 993--1017, 2010. doi: 10.1090/S0025-5718-09-02315-1
Appeared 2009
- J. Baldeaux and J. Dick, QMC Rules of Arbitrary High Order: Reproducing Kernel Hilbert space approach. Constructive Approximation, 30, 495--527, 2009. doi: 10.1007/s00365-009-9074-y
- J. Baldeaux, J. Dick, and P. Kritzer, On the approximation of smooth functions using generalized digital nets. J. Complexity, 25, 544-- 567, 2009. doi: 10.1016/j.jco.2009.07.003
- J. Dick, The decay of the Walsh coefficients of smooth functions. Bull. Austral. Math. Soc., 80, 430--453, 2009. doi: 10.1017/S0004972709000392 For an arXiv version see here.
- J. Dick and H. Niederreiter, Duality for digital sequences. J. Complexity, 25, 406--414, 2009. doi: 10.1016/j.jco.2009.06.004
- K. I. Liu, J. Dick, and F. J. Hickernell, A multivariate fast discrete Walsh transform with an application to function interpolation. Math. Comp., 78, 1573--1591, 2009. doi: 10.1090/S0025-5718-09-02202-9
- J. Dick, On quasi-Monte Carlo rules achieving higher order convergence. In: Proceedings of the MCQMC'08 conference, Montreal, Canada, P. L'Ecuyer and A. Owen (eds.), pp. 73--96, 2009. doi: 10.1007/978-3-642-04107-5_5 An earlier version can be found here.
- J. Dick and J. Baldeaux, Equidistribution properties of generalized nets and sequences. In: Proceedings of the MCQMC'08 conference, Montreal, Canada, P. L'Ecuyer and A. Owen (eds.), pp. 305--323, 2009. doi: 10.1007/978-3-642-04107-5_19 An earlier version can be found here.
Appeared 2008
- J. Dick, Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. SIAM J. Numer. Anal., 46, 1519--1553, 2008. doi: 10.1137/060666639 For a Matlab program generating higher order digital nets, numerical examples and plots of higher order digital nets see here. For the arXiv version see here.
- J. Dick, Koksma-Hlawka type inequalities of fractional order. Ann. Mat. Pura Appl., 187, 385--403, 2008. doi: 10.1007/s10231-007-0048-z
- J. Dick, P. Kritzer, and F. Y. Kuo, Approximation of Functions Using Digital Nets. In: Proceedings of the MCQMC conference 2006, Ulm, Germany, A. Keller, S. Heinrich and H. Niederreiter (Eds.), Springer Verlag, Berlin, 275--297, 2008. An earlier version can be found here.
- J. Dick and H. Niederreiter, On the exact $t-value of Niederreiter and Sobol' sequences. J. Complexity, 24, 572--581, 2008. doi: 10.1016/j.jco.2008.05.004
- J. Dick, F. Pillichshammer, and B. J. Waterhouse, The construction of good extensible rank-1 lattices. Math. Comp., 77, 2345--2373, 2008. doi: 10.1090/S0025-5718-08-02009-7
- F. J. Hickernell and J. Dick, An algorithm driven approach to error analysis for multidimensional integration. Int. J. of Num. Anal. and Modeling, 5, 167--189, 2008.
Appeared 2007
- L. L. Cristea, J. Dick, G. Leobacher, and F. Pillichshammer, The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Numer. Math., 105, 413--455, 2007. doi: 10.1007/s00211-006-0046-x
- J. Dick, Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high dimensional periodic functions. SIAM J. Numer. Anal., 45, 2141--2176, 2007. doi: 10.1137/060658916 For the arXiv version see here.
- J. Dick, The construction of extensible polynomial lattice rules with small weighted star discrepancy. Math. Comp., 76, 2077--2085, 2007. doi: 10.1090/S0025-5718-07-01984-9
- J. Dick, A note on the existence of sequences with small star discrepancy. J. Complexity, 23, 649--652, 2007. doi: 10.1016/j.jco.2007.01.004
- J. Dick, P. Kritzer, F. Y. Kuo, and I. H. Sloan, Lattice-Nyström method for Fredholm integral equations of the second kind. J. Complexity, 23, 752--772, 2007. doi: 10.1016/j.jco.2007.03.004
- J. Dick, P. Kritzer, G. Leobacher, and F. Pillichshammer, Constructions of general polynomial lattice rules based on the weighted star discrepancy. Finite Fields Appl., 13, 1045--1070, 2007. doi: 10.1016/j.ffa.2006.09.001
- J. Dick, P. Kritzer, F. Pillichshammer, and W. Ch. Schmid, On the existence of higher order polynomial lattices based on a generalized figure of merit. J. Complexity, 23, 581--593, 2007. doi: 10.1016/j.jco.2006.12.003
- J. Dick, G. Leobacher, and F. Pillichshammer, Randomized Smolyak algorithms based on digital sequences for multivariate integration. IMA J. Numer. Anal., 27, 655--674, 2007. doi: 10.1093/imanum/drm002
- J. Dick and F. Pillichshammer, Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. J. Complexity, 23, 436--453, 2007. doi: 10.1016/j.jco.2007.02.001
- J. Dick, F. Pillichshammer, and B. J. Waterhouse, The construction of good extensible Korobov rules. Computing, 79, 79--91, 2007. doi: 10.1007/s00607-006-0216-9
Appeared 2006
- L. L. Cristea, J. Dick, and F. Pillichshammer, On the mean square weighted L_2 discrepancy of randomized digital nets in prime base. J. Complexity, 22, 605--629, 2006. doi: 10.1016/j.jco.2006.03.005
- J. Dick, A Taylor space for multivariate integration. Monte Carlo Methods Appl., 12, 99--112, 2006. doi: 10.1515/156939606777488860
- J. Dick and P. Kritzer, A best possible upper bound on the star discrepancy of (t,m,2)-nets. Monte Carlo Methods Appl., 12, 1--17, 2006. doi: 10.1515/156939606776886643
- J. Dick, H. Niederreiter, and F. Pillichshammer, Weighted star discrepancy of digital nets in prime bases. In: Proceedings of the MC^2QMC conference 2004, Juan-les-Pins, France, H. Niederreiter and D. Talay (Eds.), Springer Verlag, Berlin, 77--96, 2006. An earlier version can be found here.
- J. Dick and F. Pillichshammer, Periodic functions with bounded remainder. Arch. Math. (Basel), 87, 554--563, 2006. doi: 10.1007/s00013-006-1837-0
- J. Dick, I. H. Sloan, X. Wang, and H. Wo\'zniakowski, Good lattice rules in weighted Korobov spaces with general weights. Numer. Math., 103, 63--97, 2006. doi: 10.1007/s00211-005-0674-6
- G. Pirsic, J. Dick, and F. Pillichshammer, Multivariate integration in weighted Sobolev spaces with cyclic nets and hyperplane nets. SIAM J. Numer. Anal., 44, 385--411, 2006. doi: 10.1137/050622638
Appeared 2005
- J. Dick and P. Kritzer, Star discrepancy estimates for digital (t,m,2)-nets and (t,2)-sequences over Z_2. Acta Math. Hungar., 109, 239--254, 2005. doi: 10.1007/s10474-005-0243-6
- J. Dick, F. Y. Kuo, F. Pillichshammer, and I. H. Sloan, Construction algorithms for polynomial lattice rules for multivariate integration. Math. Comp., 74, 1895--1921, 2005. doi: 10.1090/S0025-5718-05-01742-4
- J. Dick, G. Leobacher, and F. Pillichshammer, Construction algorithms for digital nets with small weighted star discrepancy. SIAM J. Numer. Anal., 43, 76--95, 2005. doi: 10.1137/040604662
- J. Dick and F. Pillichshammer, Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. J. Complexity, 21, 149--195, 2005. doi: 10.1016/j.jco.2004.07.003
- J. Dick and F. Pillichshammer, On the mean square weighted L_2 discrepancy of randomized digital (t,m,s)-nets over Z_2. Acta Arith., 117, 371--403, 2005. doi: 10.4064/aa117-4-4
- J. Dick and F. Pillichshammer, Dyadic diaphony of digital nets over Z_2. Monatsh. Math., 145, 285--299, 2005. doi: 10.1007/s00605-004-0287-7
- J. Dick and F. Pillichshammer, The figure of merit of 2-dimensional rank 2 lattice rules. INTEGERS, Electronic Journal of Combinatorial Number Theory, 5(3), \#A05, 2005.
- J. Dick and F. Pillichshammer, Diaphony, discrepancy, spectral test and worst-case error. Math. Comput. Simulation, 70, 159--171, 2005. doi: 10.1016/j.matcom.2005.06.004
Appeared 2004
- J. Dick, On the convergence rate of the component-by-component construction of good lattice rules. J. Complexity, 20, 493--522 , 2004. doi: 10.1016/j.jco.2003.11.008
- J. Dick and F. Y. Kuo, Reducing the construction cost of the component-by-component construction of good lattice rules. Math. Comp., 73, 1967--1988, 2004. doi: 10.1090/S0025-5718-03-01610-7
- J. Dick and F. Y. Kuo, Constructing good lattice rules with millions of points. In: Proceedings of the MCQMC conference 2002, Singapore, H. Niederreiter (Ed.), Springer Verlag, Berlin, 181--197, 2004. An earlier version can be found here.
- J. Dick, I. H. Sloan, X. Wang, and H. Wo\'zniakowksi, Liberating the weights. J. Complexity, 20, 593--623, 2004. doi: 10.1016/j.jco.2003.06.002
- X. Wang, I. H. Sloan, and J. Dick, On Korobov lattice rules in weighted Korobov spaces. SIAM J. Numer. Anal., 42, 1760--1779, 2004. doi: 10.1016/j.jco.2003.06.002
