On the power of standard information for tractability for L_∞ approximation of periodic functions in the worst case setting
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We study multivariate approximation of periodic function in the worst case setting with the error measured in the L_∞ norm. We consider algorithms that use standard information Λ^ std consisting of function values or general linear information Λ^ all consisting of arbitrary continuous linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability for Λ^ std and Λ^ all under the absolute or normalized error criterion, and show that the power of Λ^ std is the same as the one of Λ^ all for some notions of algebraic and exponential tractability. Our result can be applied to weighted Korobov spaces and Korobov spaces with exponential weight. This gives a special solution to Open problem 145 as posed by Novak and Woźniakowski (2012).
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