Select Publications

Books

Dick J; Kuo FY; Woźniakowski H, 2018, Contemporary computational mathematics - a celebration of the 80th birthday of Ian Sloan, http://dx.doi.org/10.1007/978-3-319-72456-0

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

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

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

Journal articles

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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