# Simple characterizations of exponential tractability for linear multivariate problems

@article{Kritzer2019SimpleCO, title={Simple characterizations of exponential tractability for linear multivariate problems}, author={Peter Kritzer and Henryk Wozniakowski}, journal={J. Complex.}, year={2019}, volume={51}, pages={110-128} }

## 10 Citations

Exponential Tractability of Linear Tensor Product Problems

- Mathematics2018 MATRIX Annals
- 2020

In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of the problem under…

Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals

- Mathematics, Computer ScienceJ. Complex.
- 2020

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

- Mathematics, Computer ScienceJ. Complex.
- 2021

Exponential tractability of L2-approximation with function values

- Computer Science, MathematicsArXiv
- 2022

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.

On the power of standard information for tractability for L2-approximation in the average case setting

- Mathematics, Computer ScienceJ. Complex.
- 2022

On the power of standard information for tractability for L2-approximation in the randomized setting

- Mathematics, Computer ScienceContemporary Mathematics
- 2022

This work solves Open Problems 98, 101, 102 and almost solve Open Problem 100 as posed by E.Novak and H.Wo´zniakowski and investigates the equivalences of various notions of algebraic and exponential tractability in the randomized setting for Λstd and Λall for the normalized or absolute error criterion.

Tractability for Volterra problems of the second kind with convolution kernels

- MathematicsJ. Complex.
- 2021

On the power of standard information for L2-approximation in the average case setting

- MathematicsJ. Complex.
- 2020

7. Adaptive approximation for multivariate linear problems with inputs lying in a cone

- Computer Science, Mathematics
- 2019

Adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones are studied, and situations where it makes sense to infer coordinate and smoothness importance are considered.

Complexity and tractability for a class of elliptic partial integro-differential equations

- MathematicsJ. Complex.
- 2022

## References

SHOWING 1-10 OF 19 REFERENCES

Exponential convergence-tractability of general linear problems in the average case setting

- MathematicsJ. Complex.
- 2015

Average case tractability of a multivariate approximation problem

- Mathematics, Computer ScienceJ. Complex.
- 2017

Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

- MathematicsJ. Approx. Theory
- 2016

Exponential convergence and tractability of multivariate integration for Korobov spaces

- MathematicsMath. Comput.
- 2011

There are numerical integration rules which achieve an exponential convergence of the worst-case integration error of multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast.

A new criterion for tractability of multivariate problems

- Computer Science, MathematicsJ. Complex.
- 2014