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Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes W m2

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Literature cited

  1. V. M. Tikhomirov, “Best methods of approximation and interpolation of functions in the space [−1, 1],” Mat. Sb.,80, No. 2, 290–304 (1969).

    Google Scholar 

  2. A. A. Zhensykbaev, “Approximation of differentiable periodic functions by splines on a uniform subdivision,” Mat. Zametki,13, No. 6, 807–816 (1973).

    Google Scholar 

  3. N. P. Korneičuk, “Exact error bound of approximation by interpolating splines on L-metric on the classesW r p (1 ⩽ p ⩽ ∞) of periodic functions,” Anal. Math.,3, No. 2, 109–117 (1977).

    Google Scholar 

  4. Yu. N. Subbotin, “Extremal problems of the theory of approximation of functions with incomplete information,” Tr. Mat. Inst. Akad. Nauk SSSR,145, 152–168 (1980).

    Google Scholar 

  5. M. Golomb, “Approximation by periodic spline interpolants on uniform meshes,” J. Approx. Theory,1, 26–65.

  6. N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  7. A. Yu. Shadrin, “Precise estimates for uniform approximation of classes\(\tilde W_2^2\) and W 22 by interpolating cubic splines,” Variats.-Raznostn. Metody Zad. Chislenn. Anal., Novosibirsk, VTs SO, Akad. Nauk SSSR, 162–180 (1987).

  8. L. V. Taikov, “Inequalities of Kolmogorov type and best formulas for numerical differentiation,” Mat. Zametki,4, No. 2, 233–238 (1968).

    Google Scholar 

  9. G. H. Hardi, J. E. Littlewood, and G. Pólya, Inequalities [Russian translation], IL, Moscow (1948).

    Google Scholar 

  10. V. I. Levin, “Exact constants in inequalities of Kolmogorov type,” Dokl. Akad. Nauk SSSR,59, No. 4, 635–638 (1948).

    Google Scholar 

  11. A. A. Sazanov, “Asymptotics of diameters of classes of functions defined by a differential operator,” Priblizh. Funktsii Polin. Splain., Sverdlovsk, 127–139 (1985).

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Translated from Matematicheskie Zametki, Vol. 48, No. 4, pp. 132–139, October, 1990.

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Shadrin, A.Y. Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes W m2 . Mathematical Notes of the Academy of Sciences of the USSR 48, 1058–1063 (1990). https://doi.org/10.1007/BF01139609

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  • DOI: https://doi.org/10.1007/BF01139609

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