Adaptive Multidimensional Integration Based on Rank-1 Lattices

DOI10.1007/978-3-319-33507-0_20zbMath1356.65008arXiv1411.1966OpenAlexW2966552998MaRDI QIDQ2957046

Fred J. Hickernell, Lluís Antoni Jiménez Rugama

Publication date: 20 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.1966

zbMATH Keywords

numerical exampleserror boundadaptive algorithmsquasi-Monte Carlo methodsmultidimensional integrationdiscrete Fourier coefficientscubature algorithmrank-1 latticesautomatic algorithms

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items (8)

Adaptive quasi-Monte Carlo finite element methods for parametric elliptic PDEs ⋮ Local adaption for approximation and minimization of univariate functions ⋮ Reliable Adaptive Cubature Using Digital Sequences ⋮ Quasi-Monte Carlo Software ⋮ An Adaptive Algorithm Employing Continuous Linear Functionals ⋮ Reliable error estimation for Sobol' indices ⋮ Adaptive Quasi-Monte Carlo Methods for Cubature ⋮ Fast automatic Bayesian cubature using lattice sampling

Uses Software

• GAIL
• GitHub
• Lattice Builder

Cites Work

• Tractability of multivariate problems. Volume II: Standard information for functionals.
• The existence of good extensible rank-1 lattices
• The cost of deterministic, adaptive, automatic algorithms: cones, not balls
• Reliable Adaptive Cubature Using Digital Sequences
• On tractability of weighted integration over bounded and unbounded regions in ℝ^{𝕤}
• High-dimensional integration: The quasi-Monte Carlo way
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