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Optimal Quadrature Formulas and Interpolation Splines Minimizing the Semi-Norm in the Hilbert Space $$K_{2}(P_{2})$$

In: Analytic Number Theory, Approximation Theory, and Special Functions

Author

Listed:
  • Abdullo R. Hayotov

    (National University of Uzbekistan, Institute of Mathematics
    University of Santiago de Compostela, Facultade de Matematicas)

  • Gradimir V. Milovanović

    (Institute of Mathematics & Serbian Academy of Sciences and Arts)

  • Kholmat M. Shadimetov

    (National University of Uzbekistan, Institute of Mathematics)

Abstract

In this paper we construct the optimal quadrature formulas in the sense of Sard, as well as interpolation splines minimizing the semi-norm in the space $$K_{2}(P_{2})$$ , where $$K_{2}(P_{2})$$ is a space of functions $$\varphi$$ which $$\varphi ^{\prime}$$ is absolutely continuous and $$\varphi ^{\prime\prime}$$ belongs to L 2(0, 1) and $$\int _{0}^{1}{(\varphi ^{\prime\prime}(x) {+\omega }^{2}\varphi (x))}^{2}dx

Suggested Citation

  • Abdullo R. Hayotov & Gradimir V. Milovanović & Kholmat M. Shadimetov, 2014. "Optimal Quadrature Formulas and Interpolation Splines Minimizing the Semi-Norm in the Hilbert Space $$K_{2}(P_{2})$$," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 573-611, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_22
    DOI: 10.1007/978-1-4939-0258-3_22
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