학술논문
On the power of standard information for tractability for $L_\infty$ approximation of periodic functions in the worst case setting.
Document Type
Journal
Author
Geng, Jiaxin (PRC-CAP-SM) AMS Author Profile; Wang, Heping (PRC-CAP-SM) AMS Author Profile
Source
Subject
46 Functional analysis -- 46E Linear function spaces and their duals
46E22Hilbert spaces with reproducing kernels
65Numerical analysis -- 65D Numerical approximation and computational geometry
65D15Algorithms for functional approximation
65Numerical analysis -- 65Y Computer aspects of numerical algorithms
65Y20Complexity and performance of numerical algorithms
46E22
65
65D15
65
65Y20
Language
English
Abstract
In this very interesting paper the authors study various notions of tractability for approximation (or optimal recovery) of functions in the uniform norm. It is proved that quite often function values give the same tractability results as general linear information. For such results one needs suitable algorithms and new upper bounds. The authors use weighted least squares methods and a subsampling technique to get improved upper bounds. Here the authors continue the recent work of M. Dolbeault, D.~W. Krieg and M. Ullrich [Appl. Comput. Harmon. Anal. {\bf 63} (2023), 113--134; MR4525968].