Сравнение скорости сходимости быстрых разложений с разложениями в классический ряд Фурье

Authors

  • Александр Данилович Чернышов Voronezh State University of Engineering Technologies image/svg+xml
  • Виталий Валерьевич Горяйнов Voronezh State Technical University image/svg+xml
  • Олег Владимирович Лешонков Joint-stock company “NIIET”
  • Елена Александровна Соболева Voronezh State University of Engineering Technologies image/svg+xml
  • Ольга Юрьевна Никифорова Voronezh State University of Engineering Technologies image/svg+xml

DOI:

https://doi.org/10.17308/sait.2019.1/1273

Keywords:

fast expansions, Fourier series, of Fourier coefficients, computing experiment, an error of evaluations, a velocity of convergence of a series

Abstract

Numerical comparison shows the great superiority of fast expansions in comparison with expansions in the classical Fourier series. The experiments were carried out for smooth functions, functions with a sharp increase and for a rapidly oscillating function. Comparison data showed that in order to achieve the same accuracy, in some cases in fast decompositions it is sufficient to take into account about 1000 times less terms than the classical Fourier series. In addition, rapid expansions admit a finite number of term-by-term differentiation, whereas classical Fourier series in the general case do not admit such differentiation.

Author Biographies

  • Александр Данилович Чернышов, Voronezh State University of Engineering Technologies

    the doctor of physical and mathematical sciences, the professor, Voronezh State University of Engineering Technologies, Department of higher mathematics and information technology

  • Виталий Валерьевич Горяйнов, Voronezh State Technical University

    the candidate of physical and mathematical sciences, associate professor, Voronezh State Technical University, Department of Applied Mathematics and Mechanics

  • Олег Владимирович Лешонков, Joint-stock company “NIIET”

    ngineer position Joint-stock company “NIIET”, Vorinezh

  • Елена Александровна Соболева, Voronezh State University of Engineering Technologies

    the candidate of physical and mathematical sciences, associate professor, Voronezh State University of Engineering Technologies, Department of higher mathematics and information technology

  • Ольга Юрьевна Никифорова, Voronezh State University of Engineering Technologies

    senior lecturer, Voronezh State University of Engineering Technologies, Department of higher mathematics and information technology

References

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Published

2019-01-18

Issue

No. 1 (2019): January - March

Section

Mathematical Methods of System Analysis and Management

License

Условия передачи авторских прав in English

How to Cite

Сравнение скорости сходимости быстрых разложений с разложениями в классический ряд Фурье. (2019). Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies, 1, 27-34. https://doi.org/10.17308/sait.2019.1/1273

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