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On asymptotically optimal weight quadrature formulas on classes of differentiable functions

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Abstract

We investigate the problem of asymptotically optimal quadrature formulas with continuous weight function on classes of differentiable functions.

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References

  1. N. P. Komeichuk, Extremal Problems in Approximation Theory [in Russian], Nauka. Moscow (1976).

    Google Scholar 

  2. S. M. Nikol’skii, Quadrature Formulas [in Russian] Nauka, Moscow 1979.

    Google Scholar 

  3. N. P. Komeichuk and A. A. Ligun, “On an estimate of the error of spline interpolation in the integral metric,” Ukr. Mat. Zh., 33, No. 5, 391–394 (1981).

    Google Scholar 

  4. A. A. Ligun, “On deviation of interpolating splines on classes of differentiable functions,” in: Investigation of Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1985), pp. 25–32.

    Google Scholar 

  5. Yu. N. Subbotin and N. I. Chernykh, “On the order of the best spline approximations of certain classes of functions,” Mat. Zametki, 7, No. 1, 31–12 (1970).

    MATH  MathSciNet  Google Scholar 

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

  7. A. A. Ligun and A. A. Shumeiko, “On the choice of nodes for the approximation of functions by splines of the best approximation,” in: Investigation of Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1985), pp. 32–39.

    Google Scholar 

  8. D. D. Pence, “Further asymptotic properties of best approximation by splines,” J. Approxim. Theory, 47, 1–17 (1987).

    Article  MathSciNet  Google Scholar 

  9. A. A. Ligun and A. A. Shumeiko, “On the optimal choice of nodes for the approximation of functions by interpolating splines,” Zh. Vychisl. Mat. Mat. Fiz., 24, No. 9, 1283–1293 (1984).

    MathSciNet  Google Scholar 

  10. A. A. Shumeiko, “On the choice of nodes for interpolating parabolic splines,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 4, 67–71 (1990).

  11. B. D. Bojanov, “Uniqueness of the optimal nodes of a quadrature formula,” Math. Comp., 36, No. 154, 532–546 (1981).

    Article  MathSciNet  Google Scholar 

  12. V. P. Motomyi, A. A. Ligun, and V. G. Doronin, Optimal Reconstruction of Functions and Functionals [in Russian] Dnepropetrovsk University, Dnepropetrovsk 1994.

    Google Scholar 

  13. V. P. Motornyi, “Investigations of Dnepropetrovsk mathematicians related to the optimization of quadrature formulas,” Ukr. Mat. Zh., 42, No. 1, 18–33 (1990).

    Article  MathSciNet  Google Scholar 

  14. S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics [in Russian], Nauka, Moscow (1976).

    Google Scholar 

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Ligun, A.A., Shumeiko, A.A. On asymptotically optimal weight quadrature formulas on classes of differentiable functions. Ukr Math J 52, 267–284 (2000). https://doi.org/10.1007/BF02529639

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  • DOI: https://doi.org/10.1007/BF02529639

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