Tractability through increasing smoothness

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Tractability through increasing smoothness
We prove that some multivariate linear tensor product problems are tractable in the worst case setting if they are defined as tensor products of univariate problems with logarithmically increasing smoothness. This is demonstrated for the approximation problem defined over Korobov spaces and for the approximation problem of certain diagonal operators. For these two problems we show necessary and sufficient conditions on the smoothness parameters of the univariate problems to obtain strong polynomial tractability. We prove that polynomial tractability is equivalent to strong polynomial tractability, and that weak tractability always holds for these problems. Under a mild assumption, the Korobov space consists of periodic functions. Periodicity is crucial since the approximation problem defined over Sobolev spaces of non-periodic functions with a special choice of the norm is not polynomially tractable for all smoothness parameters no matter how fast they go to infinity. Furthermore, dep...
Anargyros Papageorgiou, Henryk Wozniakowski
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JC
Authors Anargyros Papageorgiou, Henryk Wozniakowski
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