SPLINE-INTERFLETATION METHOD IN FINDING THE LARGEST (SMALLEST) VALUE OF THE FUNCTION OF THREE VARIABLES IN MULTIEXTREMAL PROBLEMS

DOI https://doi.org/10.15407/pmach2017.03.040
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 3, 2017 (September)
Pages 40-48
Cited by J. of Mech. Eng., 2017, vol. 20, no. 3, pp. 40-48

 

Authors

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine), e-mail: academ_mail@ukr.net

O. V. Yarmosh, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine)

T. I. Chorna, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine), e-mail: tanya_chorna@ukr.net

 

Abstract

This article proposes to use spline-interlineation operators on a system of mutually perpendicular straight lines, constructed using spline-interfletation operators of three variables to solve the problem of finding the largest and smallest values of a continuous function of three variables in a closed domain D=[0, 1]3. An example is considered. An analysis of the computational experiment is given.

 

Keywords: spline-interlineation operators, spline-interfletation operators, function traces, mutually perpendicular straight lines

 

References

  1. Mihalevich, M. V. (2005). Modelirovanie perehodnoj jekonomiki: modeli, metody, informacionnye tehnologii. Kiyev: Nauk. dumka, 669 p.
  2. Gavriljuk, I. P. & Makarov, V. L. (1995). Metodi obchislen’, Pіdruchnik: U 2ch. Kyiv: Vishha shk., Ch. 1, 367 p.
  3. Gavriljuk, I. P. & Makarov, V. L. (1995). Metodi obchislen’, Pіdruchnik: U 2ch. Kyiv: Vishha shk., Ch. 2, 431 p.
  4. Makarov, V. L. & Khlobistov, V. V. (2000). Interpolirovanie operatorov. Kiyev: Nauk. dumka, 406.
  5. Litvin, O. N. (1988). Interpolirovanie funkcij, Ucheb.posobie. Kiyev: UMK VO, 32 p.
  6. Litvin, O. M. (2002). Іnterlіnacіja funkcії ta dejakі її zastosuvannja. Kharkіv: Osnova, 544 p.
  7. Litvin, O. M. & Gulik, L. I. (2011). Іnterfletacіja funkcіj pri rozv’jazuvannі trivimіrnoї zadachі teploprovіdnostі. Kyiv: Nauk. dumka, 210 p.
  8. Litvin, O. M, Yarmosh, O. V., & Chorna, T. I. (2016). Metod splajn-interlinacii pri znahodzhennsi najbil’shih (najmenshih) znachen’ funkcii dvoh zminnih v zamknutij oblasti. Bionika intellekta, no. 2(87), pp. 77–82.

 

Received 11 April 2017

Published 30 September 2017