Adaptive Quasi-Monte Carlo Methods for Cubature

DOI10.1007/978-3-319-72456-0_27zbMath1405.65011arXiv1702.01491OpenAlexW2586480345MaRDI QIDQ4611818

Lluís Antoni Jiménez Rugama, Fred J. Hickernell, Da Li

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/1702.01491

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical quadrature and cubature formulas (65D32)

Related Items (2)

Quasi-Monte Carlo Software ⋮ Reliable error estimation for Sobol' indices

Uses Software

• Matlab
• GAIL

Cites Work

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• On the \(L_2\)-discrepancy for anchored boxes
• Reliable error estimation for Sobol' indices
• On tractability of linear tensor product problems for \(\infty \)-variate classes of functions
• Control variates for quasi-Monte Carlo (with comments and rejoinder)
• Multilevel Monte Carlo Methods
• Reliable Adaptive Cubature Using Digital Sequences
• Adaptive Multidimensional Integration Based on Rank-1 Lattices
• On the Warnock-Halton quasi-standard error
• A generalized discrepancy and quadrature error bound
• Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature
• Implementation and tests of low-discrepancy sequences
• Accelerating the Convergence of Lattice Methods by Importance Sampling-Based Transformations
• High-dimensional integration: The quasi-Monte Carlo way
• Quasi-Probability: Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically
• Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

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