Using reserves for computation optimization to improve the integration of rapidly oscillating functions



We present a theory of evaluating integrals of rapidly oscillating functions in various classes of subintegral functions with the use of a mesh information operator on subintegral functions. The theory allows us to derive and prove optimal (with respect to accuracy and (or) performance) and nearly optimal quadrature formulas and to test their quality against well-known and proposed numerical integration algorithms and to determine their efficiency domains. A technique is proposed to determine the optimal parameters of computational algorithms that obtain the ε-solution of the problem.


integrals of rapidly oscillating functions quadrature formulas optimal algorithms quality characteristic testing ε-solution of a problem 


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • V. K. Zadiraka
    • 1
  • S. S. Melnikova
    • 1
  • L. V. Luts
    • 1
  1. 1.V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of UkraineKyivUkraine

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