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

Abdullo R. Hayotov (), Gradimir V. Milovanović () and Kholmat M. Shadimetov ()
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Abdullo R. Hayotov: National University of Uzbekistan, Institute of Mathematics
Gradimir V. Milovanović: Institute of Mathematics & Serbian Academy of Sciences and Arts
Kholmat M. Shadimetov: National University of Uzbekistan, Institute of Mathematics

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 573-611 from Springer

Abstract: 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

Keywords: Hilbert Space; Sobolev Space; Quadrature Formula; Interpolation Spline; Interpolation Problem (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_22

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DOI: 10.1007/978-1-4939-0258-3_22

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