Prefractal as the source of new rational approximations of functions with a fractal representation
The Article is devoted to the problem of accelerating the convergence of polynomial and rational approximations of functions. In the theory of approximation of functions often used the idea of reducing the interval change in the argument as a method to accelerate the convergence of exponential and r...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | Russian |
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North-Caucasus Federal University
2022-09-01
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| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/247 |
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| _version_ | 1850064718854619136 |
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| author | Petr Kirillovich Korneev Irina Alexandrovna Zhuravleva Elena Vladimirovna Nepretimova Andrey Vladimirovich Gladkov Alexei Mikhailovich Lyagin |
| author_facet | Petr Kirillovich Korneev Irina Alexandrovna Zhuravleva Elena Vladimirovna Nepretimova Andrey Vladimirovich Gladkov Alexei Mikhailovich Lyagin |
| author_sort | Petr Kirillovich Korneev |
| collection | DOAJ |
| description | The Article is devoted to the problem of accelerating the convergence of polynomial and rational approximations of functions. In the theory of approximation of functions often used the idea of reducing the interval change in the argument as a method to accelerate the convergence of exponential and rational approximations, approximating this function. In this article, using this idea, a first for this function builds a branching continued fraction, whose branches are either functional series, functional or chain fractions. In this case, the branching continued fraction representing this function is a fractal and at the same time compresses the range of variation of the argument in 2* (k = 1, 2, ...) time, where 2* is the number of branches of the branched chain fraction. That is, the computation of this function at the point x is to compute x/2k, which is natural and leads to acceleration of convergence of exponential and rational approximations. To build a new rational approximations of branching continued fraction (fractal) is replaced by prefractals - chain-branching fraction with a finite number of links. Here each link is replaced by the polynomial finite chain fraction. In the result, we can obtain arbitrarily many rational approximations. |
| format | Article |
| id | doaj-art-c1a6c84059984a56992472367ce32d09 |
| institution | DOAJ |
| issn | 2308-4758 |
| language | Russian |
| publishDate | 2022-09-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Наука. Инновации. Технологии |
| spelling | doaj-art-c1a6c84059984a56992472367ce32d092025-08-20T02:49:13ZrusNorth-Caucasus Federal UniversityНаука. Инновации. Технологии2308-47582022-09-01033342246Prefractal as the source of new rational approximations of functions with a fractal representationPetr Kirillovich Korneev0Irina Alexandrovna Zhuravleva1Elena Vladimirovna Nepretimova2Andrey Vladimirovich Gladkov3Alexei Mikhailovich Lyagin4North-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityThe Article is devoted to the problem of accelerating the convergence of polynomial and rational approximations of functions. In the theory of approximation of functions often used the idea of reducing the interval change in the argument as a method to accelerate the convergence of exponential and rational approximations, approximating this function. In this article, using this idea, a first for this function builds a branching continued fraction, whose branches are either functional series, functional or chain fractions. In this case, the branching continued fraction representing this function is a fractal and at the same time compresses the range of variation of the argument in 2* (k = 1, 2, ...) time, where 2* is the number of branches of the branched chain fraction. That is, the computation of this function at the point x is to compute x/2k, which is natural and leads to acceleration of convergence of exponential and rational approximations. To build a new rational approximations of branching continued fraction (fractal) is replaced by prefractals - chain-branching fraction with a finite number of links. Here each link is replaced by the polynomial finite chain fraction. In the result, we can obtain arbitrarily many rational approximations.https://scienceit.elpub.ru/jour/article/view/247аппроксимацияфункциональные рядыцепные дробифракталысходимостьapproximationfunctional seriescontinued fractionsfractalsconvergence |
| spellingShingle | Petr Kirillovich Korneev Irina Alexandrovna Zhuravleva Elena Vladimirovna Nepretimova Andrey Vladimirovich Gladkov Alexei Mikhailovich Lyagin Prefractal as the source of new rational approximations of functions with a fractal representation Наука. Инновации. Технологии аппроксимация функциональные ряды цепные дроби фракталы сходимость approximation functional series continued fractions fractals convergence |
| title | Prefractal as the source of new rational approximations of functions with a fractal representation |
| title_full | Prefractal as the source of new rational approximations of functions with a fractal representation |
| title_fullStr | Prefractal as the source of new rational approximations of functions with a fractal representation |
| title_full_unstemmed | Prefractal as the source of new rational approximations of functions with a fractal representation |
| title_short | Prefractal as the source of new rational approximations of functions with a fractal representation |
| title_sort | prefractal as the source of new rational approximations of functions with a fractal representation |
| topic | аппроксимация функциональные ряды цепные дроби фракталы сходимость approximation functional series continued fractions fractals convergence |
| url | https://scienceit.elpub.ru/jour/article/view/247 |
| work_keys_str_mv | AT petrkirillovichkorneev prefractalasthesourceofnewrationalapproximationsoffunctionswithafractalrepresentation AT irinaalexandrovnazhuravleva prefractalasthesourceofnewrationalapproximationsoffunctionswithafractalrepresentation AT elenavladimirovnanepretimova prefractalasthesourceofnewrationalapproximationsoffunctionswithafractalrepresentation AT andreyvladimirovichgladkov prefractalasthesourceofnewrationalapproximationsoffunctionswithafractalrepresentation AT alexeimikhailovichlyagin prefractalasthesourceofnewrationalapproximationsoffunctionswithafractalrepresentation |