Integration error for multivariate functions from anisotropic classes

Authors:
Fang Gensun;Ye Peixin
Affiliations:
Department of Mathematics, Beijing Normal University, Beijing 100875, China;Department of Mathematics, Beijing Normal University, Beijing 100875, China
Venue:
Journal of Complexity
Year:
2003

Citing 6
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When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?

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Quantum summation with an application to integration

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Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms

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The complexity of function approximation on Sobolev spaces with bounded mixed derivative by linear Monte Carlo methods

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Abstract

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class Wpr(Id), Nikolskii class Wpr(Id) and their periodic analogue is obtained. It is proved that if p 1, then the stochastic and average error bounds are essentially smaller than the deterministic error bounds.Nonlinear methods, adaptive methods, or even methods with varying cardinality are not significantly better than the simplest linear method s(f) = Σi=1n cif(ai).