This paper discusses the construction of an optimal quadrature formula based on a functional approach for the numerical calculation of Fourier coefficients. In this case, first we solve the boundary value problem for the extremal function of the quadrature formula. Using the extremal function, the form of the norm of the error functional is found. The norm of the error functional depends on the coefficients and nodes. We find the minimum value of the norm of the functional based on the coefficients with given nodes. Thus, we will construct an optimal quadrature formula with in the Hilbert space. The order of approximation of the constructed quadrature formula is ????(ℎ^3) and this formula is exact for the hyperbolic sine, hyperbolic cosine and constant number.
| Mualliflar | Kurbonnazarov, A.I., Курбонназаров, А.И. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2024-12-11 |
| Son | 4/1 |
| Betlar | 46-63 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-08-27 |
quadrature formula, Fourier coefficients, error functional, extremal function, квадратурная формула, коэффициенты Фурье, функционал погрешности, экстремальная функция
| APA | Kurbonnazarov, A.I., & Курбонназаров, А.И. (2024). Optimal quadrature formula for calculating Fourier coefficients in Hilbert space. Ҳисоблаш ва амалий математика муаммолари, (4/1), 46-63. https://journals.airi.uz/index.php/pvpm/article/view/47 |
|---|---|
| GOST (OAK) | Kurbonnazarov, A.I., Курбонназаров, А.И. Optimal quadrature formula for calculating Fourier coefficients in Hilbert space // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 46-63. |
| MLA | Kurbonnazarov, A.I., and Курбонназаров, А.И. “Optimal quadrature formula for calculating Fourier coefficients in Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 46-63, 2024. https://journals.airi.uz/index.php/pvpm/article/view/47 |
| Chicago | Kurbonnazarov, A.I., and Курбонназаров, А.И. “Optimal quadrature formula for calculating Fourier coefficients in Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 46-63 (2024). https://journals.airi.uz/index.php/pvpm/article/view/47 |
| Harvard | Kurbonnazarov, A.I., and Курбонназаров, А.И (2024) ‘Optimal quadrature formula for calculating Fourier coefficients in Hilbert space’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 46-63. https://journals.airi.uz/index.php/pvpm/article/view/47 |
| BibTeX | @article{kurbonnazarovai2024,
title = {Optimal quadrature formula for calculating Fourier coefficients in Hilbert space},
author = {Kurbonnazarov, A.I. and Курбонназаров, А.И.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {46-63},
url = {https://journals.airi.uz/index.php/pvpm/article/view/47}
} |
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