Розв'язування задачі інтерпретації спостережень з використанням сплайн-наближення сканованої функції / Верлань А. Ф., Малачівський П. С., Пізюр Я. В. (2021)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2021, 57 (4))

Verlan A.F., Malachivskyy P.S., Pizyur Y.V.
Solving the problem of interpreting observations using the spline approximation of the scanned function

An accuracy analysis of the numerical implementation of the frequency method for solving the integral equation in the problem of interpreting technical observations using the spline approximation of the scanned function is presented. The algorithm for solving the integral equation of the interpretation problem, which is based on the application of the Tikhonov regularization method with the search for a solution in the frequency domain with a truncation of the frequency spectrum is investigated. To increase the accuracy of the interpretation results, the use of spline approximation of the values of the scanned function, i.e., the right-hand side of the integral equation, is proposed. The accuracy of the solution of the integral equation is estimated using the regularization method and taking into account the error accompanied by the inaccuracy of the right-hand side, as well as the error in calculating the kernel values. A method for calculating the accuracy-optimal smoothing spline approximation of the scanned function is proposed. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: accuracy estimation, Fredholm integral equation, frequency spectrum truncation, interpretation problem, spline approximation, Tikhonov regularization method, Frequency domain analysis, Numerical methods, Accuracy analysis, Algorithm for solving, Frequency domains, Frequency methods, Numerical implementation, Regularization methods, Spline approximations, Tikhonov regularization method, Integral equations


Cite:
Verlan A.F., Malachivskyy P.S., Pizyur Y.V. (2021). Solving the problem of interpreting observations using the spline approximation of the scanned function. Cybernetics and Systems Analysis, 57 (4), 95–103. doi: https://doi.org/10.1007/s10559-021-00383-5 http://jnas.nbuv.gov.ua/article/UJRN-0001254214 [In Ukrainian].


 

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