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ЧЕБИШОВСЬКЕ НАБЛИЖЕННЯ ФУНКЦІЙ БАГАТЬОХ ЗМІННИХ СТЕПЕНЕВИМ ВИРАЗОМ.

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Název: ЧЕБИШОВСЬКЕ НАБЛИЖЕННЯ ФУНКЦІЙ БАГАТЬОХ ЗМІННИХ СТЕПЕНЕВИМ ВИРАЗОМ. (Ukrainian)
Alternate Title: CHEBYSHEV APPROXIMATION OF THE MULTIVARIABLE FUNCTIONS BY POWER EXPRESSION. (English)
Autoři: МАЛАЧІВСЬКИЙ, П. С., МЕЛЬНИЧОК, Л. С., ПІЗЮР, Я. В.
Zdroj: Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz; 2024, Issue 4, p70-78, 9p
Abstrakt: A method of constructing the Chebyshev approximation with the smallest relative error of multivariable functions by a power expression is proposed. It consists in constructing an intermediate Chebyshev approximation of the function, which is the root of the corresponding power of the given function by a polynomial. The parameters of the polynomial approximation are calculated as the limiting mean-power approximation according to the iterative scheme using the least squares method with a variable weight function. Test examples are given that confirm the fast convergence of the method of constructing the Chebyshev approximation using the power expression of functions of one, two, and three variables. [ABSTRACT FROM AUTHOR]
Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Databáze: Complementary Index
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  Data: ЧЕБИШОВСЬКЕ НАБЛИЖЕННЯ ФУНКЦІЙ БАГАТЬОХ ЗМІННИХ СТЕПЕНЕВИМ ВИРАЗОМ. (Ukrainian)
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  Data: CHEBYSHEV APPROXIMATION OF THE MULTIVARIABLE FUNCTIONS BY POWER EXPRESSION. (English)
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  Data: Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz; 2024, Issue 4, p70-78, 9p
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A method of constructing the Chebyshev approximation with the smallest relative error of multivariable functions by a power expression is proposed. It consists in constructing an intermediate Chebyshev approximation of the function, which is the root of the corresponding power of the given function by a polynomial. The parameters of the polynomial approximation are calculated as the limiting mean-power approximation according to the iterative scheme using the least squares method with a variable weight function. Test examples are given that confirm the fast convergence of the method of constructing the Chebyshev approximation using the power expression of functions of one, two, and three variables. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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