Quasi-polynomial tractability

@article{Gnewuch2011QuasipolynomialT,
  title={Quasi-polynomial tractability},
  author={Michael Gnewuch and Henryk Wozniakowski},
  journal={J. Complex.},
  year={2011},
  volume={27},
  pages={312-330}
}
Uniform weak tractability
Quasi-polynomial tractability of linear problems in the average case setting
Tractability of multivariate analytic problems
TLDR
The goal of this paper is to survey the existing results, present some new results, and propose further questions for the study of tractability of multivariate analytic questions.
Simplified criterion of quasi-polynomial tractability and its applications
We study approximation properties of sequences of centered random elements $X_d$, $d\in\mathbb{N}$, with values in separable Hilbert spaces. We focus on sequences of tensor product-type random
Uniform Weak Tractability of Multivariate Problems
TLDR
This dissertation gives necessary and sufficient conditions on uniform weak tractability of homogeneous linear tensor product problems in the worst case, average case and randomized settings, and establishes necessary andsufficient conditions of those problems in terms of their regularity parameters.
...
...

References

SHOWING 1-10 OF 17 REFERENCES
Generalized tractability for multivariate problems Part I: Linear tensor product problems and linear information
Generalized Tractability for Multivariate Problems
We continue the study of generalized tractability initiated in our previous paper “Generalized tractability for multivariate problems, Part I: Linear tensor product problems and linear information”,
Tractability of Multivariate Problems
TLDR
The main purpose of this book is to study weighted spaces and to obtain conditions on the weights that are necessary and sufficient to achieve various notions of tractability, depending on how to measure the lack of exponential dependence.
On the tractability of linear tensor product problems in the worst case
Tractability and Strong Tractability of Linear Multivariate Problems
TLDR
This work provides necessary and sufficient conditions for linear multivariate problems to be tractable or strongly tractable in the worst case, average case, randomized, and probabilistic settings, and considers linearMultivariate problems over reproducing kernel Hilbert spaces, showing that such problems are strong tractable even in the best case setting.
Generalized Tractability for Multivariate Problems Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability
TLDR
Generalized tractability is obtained for T(x,y), which is a tractability function which is non-decreasing in both variables and grows slower than exponentially to infinity and which is known that T must go to infinity faster than polynomially.
Generalized Tractability for Linear Functionals
We study approximation of continuous linear functionals Id defined over reproducing kernel weighted Hilbert spaces of d-variate functions. Let n(e, Id) denote the minimal number of function values
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.
...
...