2022, Vol. 9, No. 2. - go to content...

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DOI: 10.15862/04ITOR222 (https://doi.org/10.15862/04ITOR222)

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Badalyan N.P., Sbitnev S.A., Molokin Yu.V., Chaschin Ye.A., Shmelev V.Ye. A piecewise quadratic interpolation method for a tabulated function with a continuous first derivative based on a linear combination of centrally symmetric parabolas. Russian journal of resources, conservation and recycling. 2022; 9(2). Available at: https://resources.today/PDF/04ITOR222.pdf (in Russian). DOI: 10.15862/04ITOR222

A piecewise quadratic interpolation method for a tabulated function with a continuous first derivative based on a linear combination of centrally symmetric parabolas

Badalyan Norayr Petikovich
Vladimir State University named after Aleksanr Grigorevich and Nikolai Stoletovy, Vladimir, Russia
E-mail: norayrbadalyan@mail.ru

Sbitnev Stanislav Aleksandrovich
Vladimir State University named after Aleksanr Grigorevich and Nikolai Stoletovy, Vladimir, Russia
E-mail: norayrbadalyan@mail.ru

Molokin Yurij Valentinovich
The Kovrov State Technological Academy named after V.A. Degtyarev, Kovrov, Russia
E-mail: molokin@dksta.ru

Chaschin Yevgeny Anatolievich
The Kovrov State Technological Academy named after V.A. Degtyarev, Kovrov, Russia
E-mail: kanircha@list.ru
RSCI: https://www.elibrary.ru/author_profile.asp?id=42261

Shmelev Vyacheslav Yevgenevich
Vladimir State University named after Aleksanr Grigorevich and Nikolai Stoletovy, Vladimir, Russia
E-mail: norayrbadalyan@mail.ru

Abstract. In engineering practice, it is often necessary to deal with reference and experimental data, in particular, with tabulated functional dependencies. In the course of performing technical calculations, it is often necessary to interpolate these dependencies to intermediate argument values that do not have tabular values. To reduce the error in determining the values of tabulated functions, it is customary to increase the number of array points to real values, which is not always possible. Or, in standard algorithms, before calculating the interpolating expression, logical operations are required to determine which segment the argument of the evaluated function belongs to. This significantly increases the cost of machine time. A new method of piecewise quadratic interpolation of a tabulated function with a continuous first derivative is proposed, based on a linear combination of modified centrally symmetric parabolas, which does not require logical operations to determine a partial segment of the grid of argument values during calculations. An original method of weighted minimization of the «swing» effect for uneven grids of argument values is proposed. A computational experiment was performed in the MATLAB system using the typical piecewise cubic Hermitian interpolation method with continuous first derivative pchip. Using the example of well-known reference data specifying tabular values of the main magnetization curve of sheet electrical steel 1571, the high numerical stability of the proposed method with respect to the «swing» effect and technical flexibility in its application to solve practical problems of processing tabular functional dependencies on substantially uneven grids of argument values, including with a small number of tabular points.

Keywords: data processing; numerical method; interpolation; spline; tension; induction; magnetic permeability

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