Reliable Adaptive Cubature Using Digital Sequences

DOI10.1007/978-3-319-33507-0_18zbMath1356.65006arXiv1410.8615OpenAlexW2964741545MaRDI QIDQ2957044

Lluís Antoni Jiménez Rugama, Fred J. Hickernell

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/1410.8615

zbMATH Keywords

cubaturenumerical exampleserror boundadaptive algorithmsquasi-Monte Carlo methodsmultidimensional integrationWalsh coefficientsSobol' sequencesdigital sequencesautomatic algorithms

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items

Adaptive quasi-Monte Carlo finite element methods for parametric elliptic PDEs ⋮ Local adaption for approximation and minimization of univariate functions ⋮ Adaptive Multidimensional Integration Based on Rank-1 Lattices ⋮ 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

Cites Work

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• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Monte Carlo and quasi-Monte Carlo sampling
• Adaptive Multidimensional Integration Based on Rank-1 Lattices
• On the Warnock-Halton quasi-standard error
• A generalized discrepancy and quadrature error bound
• On tractability of weighted integration over bounded and unbounded regions in ℝ^{𝕤}
• On strong tractability of weighted multivariate integration