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

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Abstract

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.

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  1. Dnepropetrovsk University, Dnepropetrovsk

    N. V. Parfinovich

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  1. N. V. Parfinovich
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Parfinovich, N.V. On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines. Ukrainian Mathematical Journal 53, 555–568 (2001). https://doi.org/10.1023/A:1012322504060

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