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Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems

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Abstract

In this paper with the help of Smolyak quadrature formulas we calculate exact orders of errors of the numerical integration of trigonometric Fourier coefficients of functions from generalized classes of Korobov and Sobolev types. We apply the obtained results to the recovery of functions from their values at a finite number of points in terms of the K. Sherniyazov approach.

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Authors and Affiliations

  1. Eurasian National University, ul. Munaitpasova 5, Astana, 010008, Republic of Kazakhstan

    N. Temirgaliev & A. A. Shomanova

  2. Southern-Kazakhstan State University, pr. Tauke-Khana 5, Shymkent, 486050, Republic of Kazakhstan

    S. S. Kudaibergenov

Authors
  1. N. Temirgaliev
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  2. S. S. Kudaibergenov
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  3. A. A. Shomanova
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Corresponding author

Correspondence to N. Temirgaliev.

Additional information

Original Russian Text © N. Temirgaliev, S.S. Kudaibergenov, and A.A. Shomanova, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 52–71.

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Temirgaliev, N., Kudaibergenov, S.S. & Shomanova, A.A. Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems. Russ Math. 54, 45–62 (2010). https://doi.org/10.3103/S1066369X10030084

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  • DOI: https://doi.org/10.3103/S1066369X10030084

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