ПАРАМЕТРИ НЕВ’ЯЗКИ АПРОКСИМАЦІЙ ДИСКРЕТНО ЗАДАНИХ ЗАЛЕЖНОСТЕЙ АНАЛІТИЧНИМИ ФУНКЦІЯМИ ТА КРИТЕРІЇ ПОШУКУ ОПТИМАЛЬНИХ ЗНАЧЕНЬ ЇХНІХ КОЕФІЦІЄНТІВ

• Date: 2021
• Main Authors: Шидловська, Н.А., Захарченко, С.М., Мазуренко, І.Л.
• Format: Article
• Language: Ukrainian
• Published: Інститут електродинаміки Національної академії наук України 2021
• Subjects: електричний опір; розрядний струм; іскроерозійне диспергування; апроксимація; нев’язка; критерії пошуку
• Online Access: https://prc.ied.org.ua/index.php/proceedings/article/view/39
• Journal Title: Proceedings of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine

Universal discrepancy parameters of approximations of discretely specified dependencies by analytical functions and search criteria for optimal values of their coefficients, as well as analysis of features of their application are described. Discrepancy parameters of approximations, which do not depend on the ranges of variation of the values of functions and the number of points of a discretely specified dependence, are proposed. They can be effective for objectively comparing the quality of approximations of any dependencies by any functions. Approximations of a discretely specified dependence of the mathematical expectation of the equivalent electrical resistance of a layer of aluminum granules during spark- erosion dispersion in water on the instantaneous values of the discharge current are carried out. As approximating func- tions, we chose a power function with an exponent factor –1 and a function based on exponential. Using the criteria of the least approximation error, the optimal values of the coefficients of both approximating functions are founded. It is shown in which cases it is advisable to use the combined search criteria for the optimal values of the coefficients of the approxi- mating functions, and in which are enough simple one-component ones. Ref. 27, fig. 2, tables 2.