The problem of constructing optimal quadrature and interpolation formulas for the approximate calculation of certain integrals and approximation of functions is one of the important problems of computational mathematics. These problems have been studied by many mathematicians and there are several methods for constructing optimal quadrature and interpolation formulas. One of these methods is the method proposed by S.L. Sobolev with the concept of an extremal function of the error functional. In this work, in a specific Hilbert space where third-order derivatives are square summable, we consider finding the extremal function of the error functional of quadrature formulas. The squared norm of the error functional will be calculated. To find the optimal coefficients, a system of linear algebraic equations is obtained. The existence and uniqueness of the resulting system is investigated. In addition, a solution to this system will be found, i.e., the optimal coefficients of the quadrature formula will be found explicitly in the space under consideration.
| Mualliflar | Shadimetov, Kh.M., Azamov, S.S., Elmuratov, G.Ch., Шадиметов, Х.M., Азамов, С.С., Элмуратов, Г.Ч. |
|---|---|
| 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 | 151-161 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
Space, extremal function, generalized function, operator, optimal quadrature formula, error functional, пространство, экстремальная функция, обобщенная функция, оптимальная квадратурная формула, функционал погрешности
| APA | Shadimetov, Kh.M., Azamov, S.S., Elmuratov, G.Ch., Шадиметов, Х.M., Азамов, С.С., & Элмуратов, Г.Ч. (2024). Minimizing the error of a quadrature formula in Hilbert space. Ҳисоблаш ва амалий математика муаммолари, (4/1), 151-161. https://journals.airi.uz/index.php/pvpm/article/view/56 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Minimizing the error of a quadrature formula in Hilbert space // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 151-161. |
| MLA | Shadimetov, Kh.M., Azamov, S.S., Elmuratov, G.Ch., Шадиметов, Х.M., Азамов, С.С., and Элмуратов, Г.Ч. “Minimizing the error of a quadrature formula in Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 151-161, 2024. https://journals.airi.uz/index.php/pvpm/article/view/56 |
| Chicago | Shadimetov, Kh.M., Azamov, S.S., Elmuratov, G.Ch., Шадиметов, Х.M., Азамов, С.С., and Элмуратов, Г.Ч. “Minimizing the error of a quadrature formula in Hilbert space.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 151-161 (2024). https://journals.airi.uz/index.php/pvpm/article/view/56 |
| Harvard | Shadimetov, Kh.M., Azamov, S.S., Elmuratov, G.Ch., Шадиметов, Х.M., Азамов, С.С., and Элмуратов, Г.Ч (2024) ‘Minimizing the error of a quadrature formula in Hilbert space’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 151-161. https://journals.airi.uz/index.php/pvpm/article/view/56 |
| BibTeX | @article{shadimetovkhm2024,
title = {Minimizing the error of a quadrature formula in Hilbert space},
author = {Shadimetov, Kh.M. and Azamov, S.S. and Elmuratov, G.Ch. and Шадиметов, Х.M. and Азамов, С.С. and Элмуратов, Г.Ч.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {151-161},
url = {https://journals.airi.uz/index.php/pvpm/article/view/56}
} |
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