On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines

• Date: 2001
• Main Authors: Parfinovych, N. V., Парфинович, Н. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4270
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain the exact asymptotics (as n → ∞) of the best L 1-approximations of classes \(W_1^r\) of periodic functions by splines s ∈ S 2n, r − 1 and s ∈ S 2n, r + k − 1 (S 2n, r is the set of 2π-periodic polynomial splines of order r and defect 1 with nodes at the points kπ/n, k ∈ Z) under certa...