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

2023/04/28 by Geng, Jiaxin, Wang, Heping
#41A63 #65C05 #65D15 #65Y20 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2304.14748

Abstract

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^{\rm std} consisting of function values or general linear information Λ^{\rm all} consisting of arbitrary continuous linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability for Λ^{\rm std} and Λ^{\rm all} under the absolute or normalized error criterion, and show that the power of Λ^{\rm std} is the same as the one of Λ^{\rm 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).

Related

• On the power of standard information for tractability for L₂-approximation in the average case setting
• Tractability of approximation in the weighted Korobov space in the worst-case setting
• Tractability of approximation in the weighted Korobov space in the worst-case setting -- a complete picture
• \boldsymbolL_∞-approximation in Korobov spaces with Exponential Weights
• On the power of standard information for tractability for L₂-approximation in the randomized setting