The curse of dimensionality for the \(L_p\)-discrepancy with finite \(p\)

DOI10.1016/J.JCO.2023.101769arXiv2303.01787OpenAlexW4379931769MaRDI QIDQ6084392

Friedrich Pillichshammer, Erich Novak

Publication date: 30 November 2023

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.01787

zbMATH Keywords

numerical integrationdiscrepancycurse of dimensionalitytractabilityquasi-Monte Carlo

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Complexity and performance of numerical algorithms (65Y20) Irregularities of distribution, discrepancy (11K38)

Cites Work

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• Covering numbers, dyadic chaining and discrepancy
• Sequences, discrepancies and applications
• Covering numbers, Vapnik-Červonenkis classes and bounds for the star-discrepancy
• On the small ball inequality in all dimensions
• Tractability of multivariate problems. Volume I: Linear information
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability of tensor product linear operators
• Intractability results for positive quadrature formulas and extremal problems for trigonometric polynomials
• Tractability properties of the discrepancy in Orlicz norms
• Lower bounds for the error of quadrature formulas for Hilbert spaces
• Lower bounds for integration and recovery in \(L_2\)
• A variant of Schur's product theorem and its applications
• Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples
• Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\)
• The BMO-discrepancy suffers from the curse of dimensionality
• Explicit constructions in the classical mean squares problem in irregularities of point distribution
• Optimal L₂discrepancy bounds for higher order digital sequences over the finite field F₂
• Harmonic analysis on totally disconnected groups and irregularities of point distributions
• On irregularities of distribution, IV
• On irregularities of distribution
• An intractability result for multiple integration
• The inverse of the star-discrepancy depends linearly on the dimension
• A generalized Faulhaber inequality, improved bracketing covers, and applications to discrepancy
• Improving a constant in high-dimensional discrepancy estimates
• A sharp discrepancy bound for jittered sampling
• Lattice Rules
• L_p- and S_p,q^rB-discrepancy of (order 2) digital nets
• On irregularities of distribution
• Note on irregularities of distribution
• Geometric discrepancy. An illustrated guide
• Intractability results for integration and discrepancy
• New lower bounds for the integration of periodic functions

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