By Professor Josef Dick

Journal articles

Dick J; Hinrichs A; Pillichshammer F, 2015, 'Proof techniques in quasi-Monte Carlo theory', Journal of Complexity, 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, 276, pp. 1 - 15, http://dx.doi.org/10.1016/j.cam.2014.08.017

Dick J; Kuo FY; Gia QTL; Schwab C; Le Gia Q, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, 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, 167, pp. 143 - 171, http://dx.doi.org/10.4064/aa167-2-4

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

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

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, 14, pp. 1027 - 1077, http://dx.doi.org/10.1007/s10208-014-9198-8

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

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

Dick J; Nuyens D; Pillichshammer F, 2014, 'Lattice rules for nonperiodic smooth integrands', Numerische Mathematik, 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, 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, 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, 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, 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984

Aistleitner C; Dick J, 2014, 'Low-discrepancy point sets for non-uniform measures', Acta Arithmetica, 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, 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, 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), 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, 30, pp. 2 - 28, http://dx.doi.org/10.1016/j.jco.2013.05.001

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, 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, 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, 141, pp. 2085 - 2096, http://dx.doi.org/10.1090/S0002-9939-2013-11490-5

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

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

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, 59, pp. 403 - 431, http://dx.doi.org/10.1007/s11075-011-9497-y

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

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

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

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

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

Baldeaux JF; Dick J; Greslehner J; Pillichshammer F, 2011, 'Construction algorithms for higher order polynomial lattice rules', Journal of Complexity, 27, pp. 281 - 299

Baldeaux JF; Dick J; Pillichshammer F, 2011, 'Duality theory and propagation rules for higher order nets', Discrete Mathematics, 311, pp. 362 - 386

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

Dick J, 2011, 'Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands', Annals of Statistics, 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, 49, pp. 1161 - 1691, http://dx.doi.org/10.1137/100789853

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

Dick J; Kritzer P, 2010, 'Duality theory and propagation rules for generalized digital nets', Mathematics of Computation, 79, pp. 993 - 1017

Liu K; Dick J; Hickernell FJ, 2009, 'A multivariate fast discrete Walsh transform with an application to function interpolation', Mathematics of Computation, 78, pp. 1573 - 1591

Dick J; Niederreiter H, 2009, 'Duality for digital sequences', Journal of Complexity, 25, pp. 406 - 414

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

Baldeaux JF; Dick J, 2009, 'QMC rules of arbitrary high order: reproducing kernel Hilbert space approach', Constructive Approximation, 30, pp. 495 - 527

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

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

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

Dick J; Niederreiter H, 2008, 'On the exact t-value of Niederreiter and Sobol` sequences', Journal of Complexity, 24, pp. 572 - 581

Dick J; Pillichshammer F; Waterhouse BJ, 2008, 'The construction of good extensible rank-1 lattices', Mathematics of Computation, 77, pp. 2345 - 2373

Dick J, 2008, 'Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order', SIAM Journal on Numerical Analysis, 46, pp. 1519 - 1553

Dick J, 2007, 'A note on the existence of sequences with small star discrepancy', Journal of Complexity, 23, pp. 649 - 652

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, 13, pp. 1045 - 1070

Dick J, 2007, 'Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions', SIAM Journal on Numerical Analysis, 45, pp. 2141 - 2176

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