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Approximation of Functions from a Hilbert Space Using Function Values or General Linear Information

  • Ralph Tandetzky
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)

Abstract

We give an example of a Hilbert space embedding \(H \subset {\mathcal{l}}_{p}\), \(1 \leq p < \infty \), whose approximation numbers tend to zero much faster than its sampling numbers. The main result shows that optimal algorithms for approximation that use only function evaluation can be more than polynomially worse than algorithms using general linear information.

Notes

Acknowledgements

I want to thank Erich Novak and Aicke Hinrichs for valuable discussions and ideas which lead to the results in this paper.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversity of JenaJenaGermany

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