Select Publications

Journal articles

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;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;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;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

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;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;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

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;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;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;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

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

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

Dick J;Kritzer P, 2015, 'On a projection-corrected component-by-component construction', Journal of Complexity, http://dx.doi.org/10.1016/j.jco.2015.08.001

Dick J;Kuo FY;Gia QT L;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

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

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

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;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

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

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', Journal of Mathematical Analysis and Applications, http://dx.doi.org/10.1016/j.jmaa.2015.05.079

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;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

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

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

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

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;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, 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;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;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

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, 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;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

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

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

Baldeaux J;Dick J;Leobacher G;Nuyens D;Pillichshammer F, 2012, 'Efficient calculation of the worst-case error and (fast) 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

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

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

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.2012.08.003

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

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

Baldeaux J;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

Baldeaux J;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

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

Dick J, 2011, 'Quasi-Monte Carlo numerical integration on ℝs: Digital nets and worst-case error', SIAM Journal on Numerical Analysis, vol. 49, pp. 1661 - 1691, http://dx.doi.org/10.1137/100789853

Baldeaux J;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


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