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  4. Chebyshev approximation of the steel magnetization characteristic by the sum of a linear expression and an arctangent function

Chebyshev approximation of the steel magnetization characteristic by the sum of a linear expression and an arctangent function

MMC.
2019;
Volume 6, Number 1
: pp. 77-84
https://doi.org/10.23939/mmc2019.01.077
Received: March 06, 2019
Accepted: April 08, 2019

Math. Model. Comput. Vol.6, No.1, pp.77-84 (2019)

Authors:
  1. P. Malachivskyy
  2. Ya. Pizyur
1
Centre of Mathematical Modelling of Ukrainian National Academy of Sciences; Ukrainian Akademy of Printing
2
Lviv Polytechnic National University

The properties of a Chebyshev approximation by the sum of a linear expression and an arctangent function have been investigated.  The condition has been established under which a Chebyshev approximation by this expression with the smallest absolute error and with the reproduction of the function value at the leftmost point exists and is unique.  A method of determining the parameters of this approximation has been suggested and substantiated.  The results of a Chebyshev approximation of the magnetization characteristic of electrotechnical steel by the sum of a linear expression and an arctangent function have been presented.

Chebyshev (uniform) approximation with condition
Chebyshev аlternance рoints
magnetization characteristic of steel
  1. Besarab O. B., Tugay Yu. I.  Modelling of ferroresonant process in voltage transformer by direct method.  Proceedings of the Institute of Electrodynamics NASU. 30, 87--90 (2011), (in Ukranian).
  2. Tugay Yu. I., Besarab O. B.  Model of electomagnetic voltage transformer for study of ferroresonance processes.  Scientific proceedings of VNTU. 4, 1--5 (2014), (in Ukranian).
  3. Kadomskaya K. P., Laptev O. I.  Antirezonansnyie transformatory napryazheniya. Effektivnost primeneniya.  Novosti elektrotehniki. 6 (42), 2--5 (2006), (in Russian).
  4. Malyar W. S., Dobushovska I. A.  Aproksymatsiia kharakterystyk namahnichuvannia elektrotekhnichnykh stalei splainamy druhoho poriadku.  Visnyk Natsionalnoho universytetu "Lvivska politekhnika''. Elektroenerhetychni ta elektromekhanichni systemy. 671, 67--71 (2010), (in Ukranian).
  5. Pan'kiv V. I., Tankevych E. M., Lutchyn M. M.  Approximation of magnetization curve of current transformers.  Pratsi Instytutu elektrodynamiky Natsionalnoi akademii nauk Ukrainy. 37, 82--90 (2014), (in Ukranian).
  6. Malachivskii P. S., Moncibovych B. R., Pizyur Ya. V., Khapko O. B.  Nablyzhennia kharakterystyky namahnichuvannia stali sumoiu liniinoho vyrazu i funktsii arktanhensu.  V nauk.-tekhn. konf. "Obchysliuvalni metody i systemy peretvorennia informatsii''. 30--34 (2018), (in Ukranian).
  7. Popov B. A., Tesler G. S.  Priblizhenie funktsiy dlya tehnicheskih prilozheniy.  Nauk. dumka, Kiev (1989), (in Russian).
  8. Malachivskii P. S., Skopetskii V. V.  Continuous and Smooth Minimax Spline Approximation.  Nauk. dumka, Kiev (2013), (in Ukranian).
  9. Popov B. A., Malachivskii P. S.  Nailuchshie chebyishevskie ppiblizheniya summoy mnogochlena i nelineynyh funktsiy.  Prepr. PhMI AN USSR. 85, 79 (1984), (in Russian).
  10. Malachivskii P. S.  Chebyshev approximation by the sum of a polynomial and a function with one nonlinear parameter.  Fiz.-Mat. Model. Inform. Tekhnol. 1, 134--145 (2005), (in Ukranian).
  11. Skopetskii V. V., Malachivskii P. S.  Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation.  Cybernetics and Systems Analysis. 45 (1), 58-–68 (2009).
  12. Korn G. A. and Korn T. M.  Mathematical Handbook for Scientists and Engineers.  McGraw-Hill Book Company (1968).
  13. Molotilov B. V., Mironov L. V., Petrenko A. H.  Kholodnokatanyye elektrotekhnicheskiye stali: Sprav. izd. Metallurgiya, Moscow (1989), (in Russian).
  14. Malachivskii P. S., Moncibovych B. R.  Algoritmy i programmnoye obespecheniye dlya ravnomernoy approksimatsii eksperimentalnykh dannykh.  Electronic Modeling. 33 (5), 97--106 (2011), (in Russian).