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Discontinuous information in the worst case and randomized settings

✍ Scribed by Aicke Hinrichs; Erich Novak; Henryk Woźniakowski

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
180 KB
Volume
286
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We believe that discontinuous linear information is never more powerful than continuous linear information for approximating continuous operators. We prove such a result in the worst case setting. In the randomized setting we consider compact linear operators defined between Hilbert spaces. In this case, the use of discontinuous linear information in the randomized setting cannot be much more powerful than continuous linear information in the worst case setting. These results can be applied when function evaluations are used even if function values are defined only almost everywhere.

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