Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces

DOI10.1090/mcom/3754OpenAlexW4280647373MaRDI QIDQ5041997

Yuya Suzuki, Dirk Nuyens

Publication date: 18 October 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.12639

zbMATH Keywords

convergence analysisnumerical integrationorder of convergence

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20) Numerical integration (65D30)

Related Items (1)

Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness

Uses Software

• DLMF

Cites Work

• Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions
• Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
• Weighted compound integration rules with higher order convergence for all \(N\)
• Multivariate integration over \(\mathbb{R}^s\) with exponential rate of convergence
• Tractability of multivariate problems. Volume I: Linear information
• Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability of multivariate integration for weighted Korobov classes
• Lattice rules in non-periodic subspaces of Sobolev spaces
• Liberating the weights
• Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights
• High-dimensional integration on \(\mathbb{R}^d\), weighted Hermite spaces, and orthogonal transforms
• Lattice rules for nonperiodic smooth integrands
• Periodization strategy may fail in high dimensions
• Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
• On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness
• MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM
• Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
• High-dimensional integration: The quasi-Monte Carlo way
• Constructing Embedded Lattice Rules for Multivariate Integration
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