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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| Format: | Article |
| Language: | English |
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Anhalt University of Applied Sciences
2024-11-01
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| 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. |
| format | Article |
| id | doaj-art-8203c95101ca4be89fd6d3d49a0e9abc |
| institution | DOAJ |
| 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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