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Optimal quadrature and cubature formulas for computing Fourier transform of finite functions of one class. Case of strong oscillation

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Cybernetics and Systems Analysis Aims and scope

Abstract

The paper deals with quadrature and cubature formulas, optimal and nearly optimal in accuracy, used to evaluate integrals of quickly oscillating functions in a class of bounded functions with piecewise continuous first derivatives bounded by a constant in one-and multidimensional cases. Optimal estimates for the numerical integration error and upper bounds are obtained for these integrals in case of strong oscillation of subintegral functions.

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References

  1. N. S. Bakhvalov, “On optimality of linear methods of approximating operators on convex classes of functions,” Zh. Vych. Mat. Mat. Fiz., 11, No. 4, 1014–1018 (1971).

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  2. V. K. Zadiraka, Theory of Computing Fourier Transform [in Russian], Naukova Dumka, Kyiv (1983).

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  3. V. K. Zadiraka and S. S. Mel’nikova, Digital Signal Processing [in Russian], Naukova Dumka, Kyiv (1993).

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. K. Zadiraka, S. S. Mel’nikova & L. V. Luts

Authors
  1. V. K. Zadiraka
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  2. S. S. Mel’nikova
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  3. L. V. Luts
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Corresponding author

Correspondence to V. K. Zadiraka.

Additional information

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 144–164, September–October 2007.

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Zadiraka, V.K., Mel’nikova, S.S. & Luts, L.V. Optimal quadrature and cubature formulas for computing Fourier transform of finite functions of one class. Case of strong oscillation. Cybern Syst Anal 43, 731–748 (2007). https://doi.org/10.1007/s10559-007-0098-7

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  • DOI: https://doi.org/10.1007/s10559-007-0098-7

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