Sampling numbers and function spaces

Authors:
Jan Vybíral
Affiliations:
Friedrich-Shiller Universitat, Mathematisches Institut, Ernst-Abbe-Platz 1-3, 07743 Jena, Germany
Venue:
Journal of Complexity
Year:
2007

Citing 3
Cited 4

Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Optimal approximation of elliptic problems by linear and nonlinear mappings I

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Optimal approximation of elliptic problems by linear and nonlinear mappings II

Journal of Complexity

Linear information versus function evaluations for L2-approximation

Journal of Approximation Theory
Randomized approximation of Sobolev embeddings, II

Journal of Complexity
Randomized approximation of Sobolev embeddings, III

Journal of Complexity
Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions

Journal of Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

We want to recover a continuous function f:(0,1)^d-C using only its function values. Let us assume, that f is from the unit ball of some function space (for example a fractional Sobolev space or a Besov space) and the precision of the reconstruction is measured in the norm of another function space of this type. We describe the rate of convergence of the optimal sampling method (linear as well as nonlinear) in this setting.