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Accurate estimates of deviations of spline approximations to classes of differentiable functions

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Abstract

We derive the approximation on [0, 1] of functionsf(x) by interpolating spline-functions sr(f; x) of degree 2r+1 and defect r+1 (r=1, 2,...). Exact estimates for ¦f(x)−sr(f; x) ¦ and ∥f(x)−sr(f; x)‖|c on the class WmHω for m=1, r=1, 2, ..., and m=2, 3, r=1 for the case of convex ω(t),are derived.

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Authors and Affiliations

  1. Dnepropetrovsk State University, USSR

    V. L. Velikin & N. P. Korneichuk

Authors
  1. V. L. Velikin
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  2. N. P. Korneichuk
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Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 483–494, May, 1971.

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Velikin, V.L., Korneichuk, N.P. Accurate estimates of deviations of spline approximations to classes of differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 9, 278–284 (1971). https://doi.org/10.1007/BF01094352

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  • DOI: https://doi.org/10.1007/BF01094352

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