Intractability results for integration in tensor product spaces

DOI10.1016/J.JCO.2024.101901MaRDI QIDQ6649712

Erich Novak, Friedrich Pillichshammer

Publication date: 6 December 2024

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

zbMATH Keywords

numerical integrationdiscrepancycurse of dimensionalityworst-case errorquasi-Monte Carlo

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Spaces of linear operators; topological tensor products; approximation properties (46A32) Numerical integration (65D30) Parameterized complexity, tractability and kernelization (68Q27)

Cites Work

• Title not available (Why is that?)
• Asymptotic behavior of average \(L_p\)-discrepancies
• Tractability of multivariate problems. Volume III: Standard information for operators
• Tractability of multivariate problems. Volume I: Linear information
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• 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
• Proof techniques in quasi-Monte Carlo theory
• A generalized discrepancy and quadrature error bound
• On the optimality of linear methods for operator approximation in convex classes of functions
• Theory of Reproducing Kernels
• Intractability results for integration and discrepancy
• The curse of dimensionality for the \(L_p\)-discrepancy with finite \(p\)
• New lower bounds for the integration of periodic functions

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