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Published Sep 23, 2009• 21 citations

Publisher

DOI: 10.1007/s00365-009-9075-x

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Constructive Approximation

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Frances Y. Kuo, G.W. Wasilkowski, Henryk Woźniakowski

Published Sep 23, 2009• 21 citations

Publisher

DOI: 10.1007/s00365-009-9075-x

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A note about EC-

(s,t)

-weak tractability of multivariate approximation with analytic Korobov kernels

This note is devoted to discussing multivariate approximation of continuous functions on

[0,1]^d

with analytic Korobov kernels in the worst and average case settings. We only consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We study EC-

(s, t)

-weak tractability under the absolute or normalized error criterion, and obtain necessary and sufficient conditions for

0<\min(s,t)<1

and

\max(s,t)\le 1

in the worst case setting and for

s,t>0

in the average case setting.