A Monte Carlo Method for Integration of Multivariate Smooth Functions
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Publication:5347536
DOI10.1137/16M1075557zbMath1365.65060arXiv1604.06008OpenAlexW2613650536MaRDI QIDQ5347536
Publication date: 24 May 2017
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.06008
Analysis of algorithms and problem complexity (68Q25) Monte Carlo methods (65C05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Numerical integration (65D30)
Related Items (17)
Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube ⋮ Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball ⋮ On the orthogonality of the Chebyshev-Frolov lattice and applications ⋮ Random-prime-fixed-vector randomised lattice-based algorithm for high-dimensional integration ⋮ Recovery of Sobolev functions restricted to iid sampling ⋮ Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ A Universal Median Quasi-Monte Carlo Integration ⋮ Consistency of randomized integration methods ⋮ A note on the dispersion of admissible lattices ⋮ Optimal Monte Carlo methods for \(L^2\)-approximation ⋮ Lattice rules with random \(n\) achieve nearly the optimal \(\mathcal{O}(n^{-\alpha-1/2})\) error independently of the dimension ⋮ Digital net properties of a polynomial analogue of Frolov's construction ⋮ Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces ⋮ Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration ⋮ Optimal Monte Carlo integration on closed manifolds ⋮ Optimal confidence for Monte Carlo integration of smooth functions
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