## 43 Citations

Quasi-polynomial tractability of linear problems in the average case setting

- MathematicsJ. Complex.
- 2014

Tractability of multivariate analytic problems

- Mathematics, Computer ScienceUniform Distribution and Quasi-Monte Carlo Methods
- 2014

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.

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

- Mathematics, Computer ScienceJ. Complex.
- 2020

Tractability of multivariate problems for standard and linear information in the worst case setting: Part I

- MathematicsJ. Approx. Theory
- 2016

A simplified criterion for quasi-polynomial tractability of approximation of random elements and its applications

- MathematicsJ. Complex.
- 2016

Tractability of multivariate approximation over weighted standard Sobolev spaces

- MathematicsJ. Complex.
- 2019

Simplified criterion of quasi-polynomial tractability and its applications

- Mathematics
- 2015

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

- Mathematics, Computer Science
- 2013

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

- Mathematics, Computer ScienceJ. Complex.
- 2007

Generalized Tractability for Multivariate Problems

- Mathematics
- 2005

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”,…

Finite-order weights imply tractability of linear multivariate problems

- Mathematics, Computer ScienceJ. Approx. Theory
- 2004

Tractability of Multivariate Problems

- Mathematics, Computer Science
- 2008

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

- MathematicsJ. Complex.
- 2009

Tractability and Strong Tractability of Linear Multivariate Problems

- Mathematics, Computer ScienceJ. Complex.
- 1994

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

- MathematicsFound. Comput. Math.
- 2009

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

- Mathematics
- 2008

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

- MathematicsJ. Complex.
- 2001

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.

Quasi-Monte Carlo methods can be efficient for integration over products of spheres

- MathematicsJ. Complex.
- 2005