On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines
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 certain restrictions on their derivatives.
English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 4, pp 555-568.
Citation Example: Parfinovych N. V. On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines // Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 489-500.