Product rules are optimal for numerical integration in classical smoothness spaces

DOI10.1016/j.jco.2016.09.001zbMath1354.65043arXiv1604.00261OpenAlexW3102262919MaRDI QIDQ346296

Aicke Hinrichs, Mario Ullrich, Henryk Woźniakowski, Erich Novak

Publication date: 5 December 2016

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

Full work available at URL: https://arxiv.org/abs/1604.00261

zbMATH Keywords

optimizationmultivariate approximationerror boundintegrationoptimal error boundsproduct rules

Mathematics Subject Classification ID

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

Related Items (9)

Uniform recovery of high-dimensional \(C^r\)-functions ⋮ A Monte Carlo Method for Integration of Multivariate Smooth Functions ⋮ Exponential tractability of \(L_2\)-approximation with function values ⋮ On the Wasserstein distance between classical sequences and the Lebesgue measure ⋮ Cubature Formulas for Multisymmetric Functions and Applications to Stochastic Partial Differential Equations ⋮ Algorithms and complexity for functions on general domains ⋮ Approximation methods for piecewise deterministic Markov processes and their costs ⋮ Breaking the curse for uniform approximation in Hilbert spaces via Monte Carlo methods ⋮ On a Kantorovich-Rubinstein inequality

Cites Work

• Tractability of multivariate problems. Volume I: Linear information
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Deterministic and stochastic error bounds in numerical analysis
• Gaussian quadrature formulae -- second Peano kernels, nodes, weights and Bessel functions
• Some nonlinear problems are as easy as the approximation problem
• On the approximate calculation of multiple integrals
• The curse of dimensionality for numerical integration of smooth functions
• ON THE BEST QUADRATURE FORMULA OF THE FORM $ \sum_{k=1}^np_kf(x_k)$ FOR SOME CLASSES OF DIFFERENTIABLE PERIODIC FUNCTIONS
• Numerical Evaluation of Multiple Integrals
• On the optimality of linear methods for operator approximation in convex classes of functions
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