On the best L1-approximations of functional classes by splines under restrictions imposed on their derivatives
Abstract
We find the exact asymptotics (n→∞) of the best L1-approximations of classes Wr1 of periodic functions by splines s∈S2n,r∼−1 (S2n,r∼−1 is a set of 2π-periodic polynomial splines of order r−1, defect one, and with nodes at the points kπ/n,k∈ℤ) such that V2π0s(r−1)≤1+ɛn, where {ɛn}∞n=1 is a decreasing sequence of positive numbers such that ɛnn2→∞ and ɛn→0 as n→∞.
Published
25.04.1999
How to Cite
Babenko, V. F., and N. V. Parfinovych. “On the Best L1-Approximations of Functional Classes by Splines under Restrictions Imposed on Their Derivatives”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 4, Apr. 1999, pp. 435-44, https://umj.imath.kiev.ua/index.php/umj/article/view/4629.
Issue
Section
Short communications