Quasi-Monte Carlo methods can be efficient for integration over products of spheres

DOI10.1016/j.jco.2004.07.001zbMath1079.65008OpenAlexW2075391389MaRDI QIDQ1772684

Ian H. Sloan, Frances Y. Kuo

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.jco.2004.07.001

zbMATH Keywords

convergenceSobolev spacereproducing kernel Hilbert spacesquasi-Monte Carlo methodsworst-case errortractabilityproducts of spheresmultivariate quasi-Monte Carlo integration

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (13)

Finite-order weights imply tractability of linear multivariate problems ⋮ Strong tractability of integration using scrambled Niederreiter points ⋮ Scrambled geometric net integration over general product spaces ⋮ A component-by-component approach to efficient numerical integration over products of spheres ⋮ Generalized tractability for multivariate problems. I: Linear tensor product problems and linear information ⋮ Derivatives of probability functions: unions of polyhedra and elliptical distributions ⋮ Quasi-Monte Carlo tractability of high dimensional integration over products of simplices ⋮ Sparse grid quadrature on products of spheres ⋮ Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ Quasi-polynomial tractability ⋮ Quasi-Monte Carlo tractability of integration problem in function spaces defined over products of balls ⋮ Polynomial-time algorithms for multivariate linear problems with finite-order weights: Average case setting ⋮ EC-tractability of approximation problems in function spaces defined over products of simplices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tractability of integration in non-periodic and periodic weighted tensor product Hilbert spaces
• On the convergence rate of the component-by-component construction of good lattice rules
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability and strong tractability of linear multivariate problems
• Tractability of multivariate integration for periodic functions
• Tractability of multivariate integration for weighted Korobov classes
• Tractability of tensor product linear operators
• Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
• Extremal systems of points and numerical integration on the sphere
• Component-by-component construction of good lattice rules with a composite number of points
• Liberating the weights
• Integration and approximation in arbitrary dimensions
• Spherical harmonics
• Component-by-component construction of good lattice rules
• On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
• Gleichverteilung auf Produkten von Sphären.
• Quadratures on a sphere
• Worst-case errors in a Sobolev space setting for cubature over the sphere S²
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Theory of Reproducing Kernels

This page was built for publication: Quasi-Monte Carlo methods can be efficient for integration over products of spheres