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On an optimal quadrature formula in the sense of Sard

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Abstract

In this paper we construct an optimal quadrature formula in the sense of Sard in the Hilbert space K 2(P 2). Using S.L. Sobolev’s method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space \(L_2^{(2)}(0,1)\). The obtained optimal quadrature formula is exact for the trigonometric functions sinx and cosx. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

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Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan

    Abdullo Rakhmonovich Hayotov & Kholmat Mahkambaevich Shadimetov

  2. Faculty of Computer Sciences, Megatrend University & Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

Authors
  1. Abdullo Rakhmonovich Hayotov
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  2. Gradimir V. Milovanović
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  3. Kholmat Mahkambaevich Shadimetov
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Corresponding author

Correspondence to Gradimir V. Milovanović.

Additional information

The work of the second author was supported in part by the Serbian Ministry of Science and Technological Development (Project: Approximation of integral and differential operators and applications, grant number #174015).

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Hayotov, A.R., Milovanović, G.V. & Shadimetov, K.M. On an optimal quadrature formula in the sense of Sard. Numer Algor 57, 487–510 (2011). https://doi.org/10.1007/s11075-010-9440-7

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  • DOI: https://doi.org/10.1007/s11075-010-9440-7

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