Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces

DOI10.1016/J.JCO.2020.101500zbMath1469.65019OpenAlexW3031394575MaRDI QIDQ1996881

Grzegorz W. Wasilkowski

Publication date: 26 February 2021

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

Full work available at URL: https://doi.org/10.1016/j.jco.2020.101500

zbMATH Keywords

multivariate integrationquasi-Monte CarloANOVA spaces

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Complexity and performance of numerical algorithms (65Y20)

Related Items (1)

On the effective dimension and multilevel Monte Carlo

Cites Work

• Unnamed Item
• Unnamed Item
• Very low truncation dimension for high dimensional integration under modest error demand
• A note on equivalence of anchored and ANOVA spaces; lower bounds
• Liberating the dimension for \(L_2\)-approximation
• Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
• Liberating the dimension for function approximation: standard information
• Tractability of infinite-dimensional integration in the worst case and randomized settings
• Liberating the dimension
• Infinite-dimensional quadrature and approximation of distributions
• On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\)
• Multi-level Monte Carlo algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability of multivariate integration for weighted Korobov classes
• Truncation dimension for linear problems on multivariate function spaces
• Truncation in average and worst case settings for special classes of \(\infty \)-variate functions
• \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems
• On embeddings of weighted tensor product Hilbert spaces
• Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_p\)
• Small superposition dimension and active set construction for multivariate integration under modest error demand
• Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration
• On tractability of linear tensor product problems for \(\infty \)-variate classes of functions
• Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives
• Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent
• Truncation Dimension for Function Approximation
• Effective Dimension of Some Weighted Pre-Sobolev Spaces with Dominating Mixed Partial Derivatives
• Liberating the Dimension for Function Approximation and Integration
• Equivalence of anchored and ANOVA spaces via interpolation

This page was built for publication: Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces