Tractability of approximation in the weighted Korobov space in the worst-case setting - a complete picture

@article{Ebert2021TractabilityOA,
  title={Tractability of approximation in the weighted Korobov space in the worst-case setting - a complete picture},
  author={Adrian Ebert and Friedrich Pillichshammer},
  journal={ArXiv},
  year={2021},
  volume={abs/2201.09940}
}
2 Citations

Tables from this paper

Exponential tractability of L2-approximation with function values
TLDR
The situation when the number of linear mea-surements required to achieve an error in dimension d ∈ N depends only poly-logarithmically on ε − 1 corresponds to an exponential order of convergence of the approximation error, which often happens in applications.

References

SHOWING 1-10 OF 25 REFERENCES
Tractability of Multivariate Integration for Periodic Functions
TLDR
It is shown that tractability and strong tractability in the worst case setting hold under the same assumptions on the weights of the Korobov space as for the restricted classes of quadrature rules.
Tractability of Multivariate Integration for Weighted Korobov Spaces: My 15 Year Partnership with Ian Sloan
This paper is intended as a birthday present for Ian Sloan who celebrated his 70th birthday during MCQMC’08 in Montreal. In the first paper with Ian we studied multivariate integration for the
Uniform weak tractability
Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers
TLDR
The worst case, randomized, and quantum settings are considered and it is proved that strong tractability and tractability in the class $\lall$ are equivalent and this holds under the same assumption as for the class £lall in the worst case setting.
Lattice Rules for Multivariate Approximation in the Worst Case Setting
We develop algorithms for multivariate approximation in weighted Korobov spaces of smooth periodic functions of d variables. Our emphasis is on large d. The smoothness of functions is characterized
Intractability Results for Integration and Discrepancy
TLDR
This paper proves intractability of integration (and discrepancy) if limsupd?dj=1?j/lnd=∞, as long as the weights satisfy the condition mentioned above, and introduces the notion of a decomposable kernel.
Weighted Tensor Product Algorithms for Linear Multivariate Problems
TLDR
It is shown that these multivariate problems defined over weighted tensor product Hilbert spaces of functions f of d variables are sometimes tractable even with a worst-case assurance.
Quasi-polynomial tractability
...
...