An Explicit Construction of Optimal Order Quasi--Monte Carlo Rules for Smooth Integrands

DOI10.1137/16M1060807zbMath1357.65006arXiv1601.06501OpenAlexW2266253056MaRDI QIDQ2817786

Takehito Yoshiki, Kosuke Suzuki, Takashi Goda

Publication date: 2 September 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06501

zbMATH Keywords

Sobolev spacenumerical integrationquasi-Monte Carloworst case errorkernel Hilbert spacehigher-order digital nets

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 (7)

Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube ⋮ A Tool for Custom Construction of QMC and RQMC Point Sets ⋮ 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 ⋮ Optimal order quadrature error bounds for infinite-dimensional higher-order digital sequences ⋮ Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces ⋮ An Explicit Construction of Optimal Order Quasi--Monte Carlo Rules for Smooth Integrands

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