On the power of standard information for tractability for L∞ approximation of periodic functions in the worst case setting

Abstract

We study multivariate approximation of periodic functions in the worst case setting with the error measured in the L∞ norm. We consider algorithms that use standard information Λstd consisting of function values or general linear information Λall consisting of arbitrary continuous linear functionals. We investigate equivalences of various notions of algebraic and exponential tractability for Λstd and Λall under the absolute or normalized error criterion, and show that the power of Λstd is the same as the one of Λall for various notions of algebraic and exponential tractability. Our results can be applied to weighted Korobov spaces and Korobov spaces with exponential weights. This gives a special solution to Open Problem 145 as posed by Novak and Woźniakowski (2012) [40].