Lower bounds for the error of quadrature formulas for Hilbert spaces
From MaRDI portal
Publication:2041063
DOI10.1016/j.jco.2020.101544zbMath1472.65029arXiv2004.00274OpenAlexW3110719148WikidataQ113871713 ScholiaQ113871713MaRDI QIDQ2041063
Aicke Hinrichs, David Krieg, Jan Vybíral, Erich Novak
Publication date: 15 July 2021
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.00274
positive definite matricescurse of dimensionalitySchur's product theoremnumerical integration in high dimensions
Related Items
Lower bounds for integration and recovery in \(L_2\) ⋮ A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm ⋮ A sharp upper bound for sampling numbers in \(L_2\) ⋮ The curse of dimensionality for the \(L_p\)-discrepancy with finite \(p\) ⋮ New lower bounds for the integration of periodic functions ⋮ Exponential tractability of \(L_2\)-approximation with function values ⋮ Sharp nonzero lower bounds for the Schur product theorem ⋮ C*-algebraic Schur product theorem, P\'{o}lya-Szeg\H{o}-Rudin question and Novak's conjecture
Cites Work
- Unnamed Item
- Unnamed Item
- Tractability of multivariate problems for standard and linear information in the worst case setting. I.
- On positive positive-definite functions and Bochner's theorem
- Tractability through increasing smoothness
- Tractability of multivariate problems. Volume I: Linear information
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Explicit cost bounds of algorithms for multivariate tensor product problems
- Tractability of multivariate integration for periodic functions
- Tractability of tensor product linear operators
- Intractability results for positive quadrature formulas and extremal problems for trigonometric polynomials
- How anisotropic mixed smoothness affects the decay of singular numbers for Sobolev embeddings
- A variant of Schur's product theorem and its applications
- Function values are enough for \(L_2\)-approximation
- Positive definite functions on spheres
- 4. On the power of random information
- An intractability result for multiple integration
- Tractability of Multivariate Problems for Standard and Linear Information in the Worst Case Setting: Part II
- Reproducing kernels of Sobolev spaces on ℝd and applications to embedding constants and tractability
- High-dimensional integration: The quasi-Monte Carlo way
- Intractability results for integration and discrepancy
