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Cubature Formulae Using Interlineation of Functions

In: Elements of the General Theory of Optimal Algorithms

Author

Listed:
  • Ivan V. Sergienko

    (National Academy of Sciences of Ukraine)

  • Valeriy K. Zadiraka

    (National Academy of Sciences)

  • Oleg M. Lytvyn

    (Ukrainian Engineering Pedagogics Academy)

Abstract

This chapter presents the cubature formulas for calculating the integrals of the functions of two variables, which are obtained by replacing the subintegral function by spline interlineation operators. The cubature formulas for calculating the integrals of fast-oscillating functions are also given, in which the non-oscillating factor is replaced by the corresponding spline interlineation formula. Here using integral representations of the residual terms of the approximation of differentiation functions of two and three variables with and without preservation of the class of differentiation. Creating application software sometimes costs more than the cost of the computer itself. Therefore, testing the quality of software is a very important task.

Suggested Citation

  • Ivan V. Sergienko & Valeriy K. Zadiraka & Oleg M. Lytvyn, 2021. "Cubature Formulae Using Interlineation of Functions," Springer Optimization and Its Applications, in: Elements of the General Theory of Optimal Algorithms, chapter 0, pages 253-280, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-90908-6_5
    DOI: 10.1007/978-3-030-90908-6_5
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