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Asymptotically optimal sampling schemes for periodic functions

Published online by Cambridge University Press:  24 October 2008

W. Dahmen ,
C. A. Micchelli  and
P. W. Smith
W. Dahmen
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 4800 Bielefeld, West Germany
C. A. Micchelli
Affiliation:
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
P. W. Smith
Affiliation:
Department of Mathematics, Old Dominion University, Norfolk, VA 23508, U.S.A.
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Extract

In this paper we are concerned with the following question: Given a function class , the space of L2-one periodic complex valued functions, when does sampling a function give optimal information for approximation? To make this question precise, we introduce the quantity

, where A is any mapping from ℝN and I is any continuous linear mapping from into ℝN.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 171 - 177
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Micchelli, C. A. and Rivlin, T. J.. A survey of optimal recovery. In Optimal Estimation in Approximation Theory (Plenum Press, 1976).Google Scholar
[2]Pinkus, A.. n-Widths in Approximation Theory (Springer-Verlag, 1985).CrossRefGoogle Scholar