Optimal Order of Convergence and (In)Tractability of Multivariate Approximation of Smooth Functions

We study the approximation problem for C ∞ functions f :[0,1] d →ℝ with respect to a W p m -norm. Here, m =[ m , m ,…, m ], d times, with the norm of the target space defined in terms of up to m partial derivatives with respect to all d variables. The optimal order of convergence is infinite, hence...

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Vydané v:	Constructive approximation Ročník 30; číslo 3; s. 457 - 473
Hlavní autori:	Novak, Erich, Woźniakowski, Henryk
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer-Verlag 01.12.2009
Predmet:	Analysis Mathematics Mathematics and Statistics Numerical Analysis Tractability Curse of dimensionality 41A25 41A63 Approximation of smooth functions 65Y20 Rate of convergence
ISSN:	0176-4276, 1432-0940
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