High-dimensional integration on \(\mathbb{R}^d\), weighted Hermite spaces, and orthogonal transforms
From MaRDI portal
Publication:2254682
DOI10.1016/j.jco.2014.09.002zbMath1309.65029arXiv1409.6109OpenAlexW2963374275MaRDI QIDQ2254682
Gunther Leobacher, Christian Irrgeher
Publication date: 6 February 2015
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.6109
Monte Carlo methods (65C05) Complexity and performance of numerical algorithms (65Y20) Numerical integration (65D30)
Related Items (13)
Approximation in Hermite spaces of smooth functions ⋮ Tractability of multivariate approximation defined over Hilbert spaces with exponential weights ⋮ Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces ⋮ Countable tensor products of Hermite spaces and spaces of Gaussian kernels ⋮ EC-tractability of multivariate approximation in Hermite spaces for the standard information class ⋮ MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM ⋮ Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness ⋮ Numerical weighted integration of functions having mixed smoothness ⋮ Tractability of \(L_2\)-approximation and integration in weighted Hermite spaces of finite smoothness ⋮ Small sample spaces for Gaussian processes ⋮ On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness ⋮ Truncation in average and worst case settings for special classes of \(\infty \)-variate functions ⋮ Integration in Hermite spaces of analytic functions
Cites Work
- Fast orthogonal transforms and generation of Brownian paths
- When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
- The Brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration
- Smoothness and dimension reduction in quasi-Monte Carlo methods
- Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction
- On the small balls problem for equivalent Gaussian measures
- Theory of Reproducing Kernels
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: High-dimensional integration on \(\mathbb{R}^d\), weighted Hermite spaces, and orthogonal transforms
