A note about EC-$(s,t)$-weak tractability of multivariate approximation with analytic Korobov kernels

Abstract

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.

18 pages

References in corpus (1)

• Average Case tractability of multivariate approximation with Gaussian kernels

Cited by in corpus (1)

• Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings