Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions

The article considers the possibilities of solving interpolation and approximation problems using special types of functions, such as root polynomials and root fractional rational, and provides relevant examples. It is prove, that the use of root polynomial functions is especially effective for inte...

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Main Authors: Igor Melnyk, Mykhailo Skrypka, Alina Pochynok, Olga Demyanchenko
Format: Article
Language:English
Published: Anhalt University of Applied Sciences 2024-11-01
Series:Proceedings of the International Conference on Applied Innovations in IT
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Online Access:https://icaiit.org/paper.php?paper=12th_ICAIIT_2/2_4
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author Igor Melnyk
Mykhailo Skrypka
Alina Pochynok
Olga Demyanchenko
author_facet Igor Melnyk
Mykhailo Skrypka
Alina Pochynok
Olga Demyanchenko
author_sort Igor Melnyk
collection DOAJ
description The article considers the possibilities of solving interpolation and approximation problems using special types of functions, such as root polynomials and root fractional rational, and provides relevant examples. It is prove, that the use of root polynomial functions is especially effective for interpolation and approximation of numerical dependencies with a ravine data set, and the use of root fractional rational functions gives the best results for various data sets with a more rigid functional dependence. To solve the approximation problem, a new approximation by reference points is proposed and tested. With a small number of points in the data set for the approximation problem, equal to twenty or less, the convergence of the proposed method is usually guaranteed. In general, the proposed algorithms are very universal and can be easily adapted to any complex problems. All the proposed methods are implemented and tested in the newly developed computer software created in the Python programming language.
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id doaj-art-8203c95101ca4be89fd6d3d49a0e9abc
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issn 2199-8876
language English
publishDate 2024-11-01
publisher Anhalt University of Applied Sciences
record_format Article
series Proceedings of the International Conference on Applied Innovations in IT
spelling doaj-art-8203c95101ca4be89fd6d3d49a0e9abc2025-08-20T03:12:40ZengAnhalt University of Applied SciencesProceedings of the International Conference on Applied Innovations in IT2199-88762024-11-0112299106http://dx.doi.org/10.25673/118122Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational FunctionsIgor Melnyk0https://orcid.org/0000-0003-0220-0615Mykhailo Skrypka1https://orcid.org/0009-0006-7142-5569Alina Pochynok2https://orcid.org/0000-0001-9531-7593Olga Demyanchenko3https://orcid.org/0000-0002-4693-0364Department of Electronic Devices and Systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteiska Avenue 37, 03056 Kyiv, UkraineDepartment of Electronic Devices and Systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteiska Avenue 37, 03056 Kyiv, UkraineResearch Institute of Electronics and Microsystems Engineering, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteiska Avenue 37, 03056 Kyiv, Ukraine Institute of Applied Mathematics and Fundamental Sciences of the National University "Lviv Polytechnic", Mytropolyta Andreia Str. 5, Building 4, 79016 Lviv, Ukraine The article considers the possibilities of solving interpolation and approximation problems using special types of functions, such as root polynomials and root fractional rational, and provides relevant examples. It is prove, that the use of root polynomial functions is especially effective for interpolation and approximation of numerical dependencies with a ravine data set, and the use of root fractional rational functions gives the best results for various data sets with a more rigid functional dependence. To solve the approximation problem, a new approximation by reference points is proposed and tested. With a small number of points in the data set for the approximation problem, equal to twenty or less, the convergence of the proposed method is usually guaranteed. In general, the proposed algorithms are very universal and can be easily adapted to any complex problems. All the proposed methods are implemented and tested in the newly developed computer software created in the Python programming language.https://icaiit.org/paper.php?paper=12th_ICAIIT_2/2_4interpolationapproximationravine dependencestiff dependenceroot-polynomial function
spellingShingle Igor Melnyk
Mykhailo Skrypka
Alina Pochynok
Olga Demyanchenko
Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
Proceedings of the International Conference on Applied Innovations in IT
interpolation
approximation
ravine dependence
stiff dependence
root-polynomial function
title Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
title_full Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
title_fullStr Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
title_full_unstemmed Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
title_short Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions
title_sort novel computer software for interpolation and approximation of ravine and stiff digital dependencies using root polynomoal and root fractional rational functions
topic interpolation
approximation
ravine dependence
stiff dependence
root-polynomial function
url https://icaiit.org/paper.php?paper=12th_ICAIIT_2/2_4
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