A note about EC-$(s,t)$-weak tractability of multivariate approximation with analytic Korobov kernels
For researchers in information-based complexity, this provides a theoretical characterization of tractability for a specific kernel class, but the results are incremental extensions of existing tractability frameworks.
The paper studies multivariate approximation with analytic Korobov kernels and establishes necessary and sufficient conditions for EC-(s,t)-weak tractability under worst-case and average-case settings, covering specific ranges of s and t.
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.