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On lower bounds for the approximation of functions by local splines with nonfixed nodes

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For functions integrable to the power \(\beta = (r + 1 + 1/p)^{ - 1} \), we obtain asymptotically exact lower bounds for the approximation by local splines of degree r and defect k< r/2 in the metric of L p

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References

  1. A. A. Ligun, “On one property of interpolation spline functions,” Ukr. Mat. Zh., 32, No. 4, 507–514 (1980).

    MATH  MathSciNet  Google Scholar 

  2. I. S. Azarin and V. I. Barmin, “Approximation by piecewise-linear functions,” in: Collection of Mathematical Works [in Russian], Naukova Dumka, Kiev (1976), pp. 25–26.

    Google Scholar 

  3. A. I. Grebennikov, “On the choice of nodes in the approximation of functions by splines,” Zh. Vych. Mat. Mat. Fiz., 16, No. 1, 219–223 (1976).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Ligun and V. F. Storchai, “On the best choice of nodes in the interpolation of functions by Hermitian splines,” Ann. Math., 2, 267–275 (1976).

    Article  Google Scholar 

  5. A. A. Ligun and V. F. Storchai, “On the best choice of nodes in the approximation of functions by local Hermitian splines,” Ukr. Mat. Zh.. 32, No. 6, 824–830 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. A. Ligun and A. A. Shumeiko, “Optimal choice of nodes in the approximation of functions by splines,” Dokl. Akad. Nauk Ukr.SSR, Ser A. No. 6, 18–22 (1984).

  7. D. Lee, “A simple approach to cardinal Lagrange and periodic Lagrange splines,” J. Approxim. Theory. 47, 93–100 (1986).

    Article  MATH  Google Scholar 

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  1. A. A. Shumeiko
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Shumeiko, A.A. On lower bounds for the approximation of functions by local splines with nonfixed nodes. Ukr Math J 52, 148–160 (2000). https://doi.org/10.1007/BF02514143

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  • DOI: https://doi.org/10.1007/BF02514143

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