Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces
From MaRDI portal
Publication:5041997
DOI10.1090/mcom/3754OpenAlexW4280647373MaRDI QIDQ5041997
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
Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20) Numerical integration (65D30)
Related Items (1)
Uses Software
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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces
