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

Нурлан Т Темиргалиев, Sabit Sarypbekovich Kudaibergenov, A. A. Shomanova

2010

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DOI 10.3103/s1066369x10030084
Data confidence 70 medium
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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.