An Upper Bound of the Minimal Dispersion via Delta Covers

DOI10.1007/978-3-319-72456-0_50zbMath1405.65025arXiv1701.06430OpenAlexW2582682870MaRDI QIDQ4611843

Daniel Rudolf

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.06430

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Combinatorial geometries and geometric closure systems (51D20) Irregularities of distribution, discrepancy (11K38)

Related Items

Universal discretization, New bounds on the minimal dispersion, Minimal dispersion of large volume boxes in the cube, Deterministic constructions of high-dimensional sets with small dispersion, Connections between numerical integration, discrepancy, dispersion, and universal discretization, Deviation from equidistance for one-dimensional sequences, The minimal spherical dispersion, The minimal \(k\)-dispersion of point sets in high dimensions, On the fixed volume discrepancy of the Fibonacci sets in the integral norms, Expected dispersion of uniformly distributed points, Improved dispersion bounds for modified Fibonacci lattices, On the fixed volume discrepancy of the Korobov point sets, A generalized Faulhaber inequality, improved bracketing covers, and applications to discrepancy, Recovery algorithms for high-dimensional rank one tensors, Smooth fixed volume discrepancy, dispersion, and related problems, The VC-dimension of axis-parallel boxes on the torus, A remark on the minimal dispersion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
• Approximation of high-dimensional rank one tensors
• Tractability of multivariate problems. Volume III: Standard information for operators
• On the maximum empty rectangle problem
• Tractability of multivariate problems. Volume I: Linear information
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Mining for empty spaces in large data sets.
• A note on minimal dispersion of point sets in the unit cube
• Quasi-Monte-Carlo methods and the dispersion of point sequences
• On the largest empty axis-parallel box amidst \(n\) points
• A lower bound for the dispersion on the torus
• On the size of the largest empty box amidst a point set
• Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy
• Some Results on the Complexity of Numerical Integration
• Learnability and the Vapnik-Chervonenkis dimension
• The inverse of the star-discrepancy depends linearly on the dimension
• Tractability of the approximation of high-dimensional rank one tensors