Numerical integration in log-Korobov and log-cosine spaces

DOI10.1007/s11075-015-9972-yzbMath1339.65008arXiv1411.2715OpenAlexW2020675975MaRDI QIDQ907580

Friedrich Pillichshammer, Peter Kritzer, Gunther Leobacher, Josef Dick

Publication date: 25 January 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.2715

zbMATH Keywords

numerical integrationreproducing kernel Hilbert spacesquasi-Monte Carlo methodsKorobov spacesworst-case errortractabilitytent transformationlattice point ruleslog-cosine spaceslog-Korobov spaces

Mathematics Subject Classification ID

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

Related Items (1)

Proof techniques in quasi-Monte Carlo theory

Cites Work

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• A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights
• On the convergence rate of the component-by-component construction of good lattice rules
• Tractability of multivariate problems. Volume I: Linear information
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Tractability of multivariate integration for periodic functions
• Tractability of multivariate integration for weighted Korobov classes
• Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
• Lattice rules for nonperiodic smooth integrands
• Component-by-component construction of good lattice rules
• The construction of good extensible rank-1 lattices
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• A generalized discrepancy and quadrature error bound
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
• Introduction to Quasi-Monte Carlo Integration and Applications
• High-dimensional integration: The quasi-Monte Carlo way
• Constructing Embedded Lattice Rules for Multivariate Integration
• Theory of Reproducing Kernels

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