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Approximation by cubic splines in the classes of continuously differentiable functions

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Abstract

The problem of approximating continuously differentiable periodic functionsf(x) by cubic interpolation splines sn(f; x) with equidistant nodes is considered. Asymptotically exact estimates for ∥f(x)-sn(f; x)∥C are obtained in the classes of functions W1Hω.

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Authors and Affiliations

  1. Dnepropetrovsk State University, USSR

    V. L. Velikin

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  1. V. L. Velikin
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 215–226, February, 1972.

In conclusion, I am deeply grateful to N. P. Korneichuk for a number of valuable remarks and conjectures utilized while working on this paper.

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Velikin, V.L. Approximation by cubic splines in the classes of continuously differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 11, 133–140 (1972). https://doi.org/10.1007/BF01097932

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  • DOI: https://doi.org/10.1007/BF01097932

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