Multivariate integration in \(C^{\infty}([0,1]^{d})\) is not strongly tractable.

DOI10.1016/S0885-064X(03)00069-4zbMath1057.68043arXiv0803.0441OpenAlexW1971345739MaRDI QIDQ1426049

Jakub Onufry Wojtaszczyk

Publication date: 14 March 2004

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

Full work available at URL: https://arxiv.org/abs/0803.0441

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25)

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The curse of dimensionality for numerical integration of smooth functions, Approximation of infinitely differentiable multivariate functions is not strongly tractable, ABC on IBC, Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions, The curse of dimensionality for numerical integration of smooth functions. II, On weak tractability of the Clenshaw-Curtis Smolyak algorithm, Computational complexity of the integration problem for anisotropic classes, Approximation of infinitely differentiable multivariate functions is intractable

Cites Work

• Open problems for tractability of multivariate integration.
• On the optimality of linear methods for operator approximation in convex classes of functions
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