Optimal importance sampling for the approximation of integrals

DOI10.1016/j.jco.2009.11.003zbMath1191.65003OpenAlexW2063850653MaRDI QIDQ964918

Aicke Hinrichs

Publication date: 21 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.jco.2009.11.003

zbMATH Keywords

importance samplingMonte Carlo methodreproducing kernel Hilbert spacesmultivariate integrationtractabilityworst case errorPietsch domination theoremrandomized setting

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items

On a Metropolis-Hastings importance sampling estimator, A Monte Carlo Method for Integration of Multivariate Smooth Functions, Lower bounds for the complexity of linear functionals in the randomized setting, Some Results on the Complexity of Numerical Integration, On weighted Hilbert spaces and integration of functions of infinitely many variables, Tractability of infinite-dimensional integration in the worst case and randomized settings, Worst-case recovery guarantees for least squares approximation using random samples, Optimal Monte Carlo integration on closed manifolds

Cites Work

• Tractability of integration in non-periodic and periodic weighted tensor product Hilbert spaces
• Tractability of multivariate problems. Volume I: Linear information
• New averaging technique for approximating weighted integrals
• On polynomial-time property for a class of randomized quadratures
• On subspaces of L\(^p\)
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