EC-(t1,t2)-tractability of approximation in weighted Korobov spaces in the worst case setting

Abstract

We investigate multivariate approximation problems in the weighted Korobov spaces in the worst case setting. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We discuss the exponential convergence-(t1,t2)-weak tractability (EC-(t1,t2)-WT) under the absolute or normalized error criterion. Especially, we give the sufficient and necessary conditions for EC-WT and EC-(t1,1)-WT with t1<1.