There are algebraic and variational approaches of construction in the spline theory. In algebraic approach splines are considered as some smooth piecewise polynomial functions. In the variational approach splines are elements of Hilbert or Banach spaces minimizing certain functionals. Then we study the problems of existence, uniqueness, and convergence of splines and algorithms for constructing them based on their own properties of splines. In this paper, we study the problem of constructing an optimal interpolation formula in a Hilbert space. Here, using the Sobolev method, the first part of the problem is solved, i.e. an explicit expression of the square of the norm of the error functional is found and a system of linear algebraic equations for the coefficients of the optimal interpolation formula is obtained.
| Mualliflar | Shadimetov, Kh.M., Atamuradova, B.M., Шадиметов, Х.М., Атамурадова, Б.М. |
|---|---|
| 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 | 64-73 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-08-27 |
Hilbert space, extremal function, error functional, interpolation formula
| APA | Shadimetov, Kh.M., Atamuradova, B.M., Шадиметов, Х.М., & Атамурадова, Б.М. (2024). Discrete system of Wiener–Hopf type for coefficients of interpolation formulas. Ҳисоблаш ва амалий математика муаммолари, (4/1), 64-73. https://journals.airi.uz/index.php/pvpm/article/view/49 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Discrete system of Wiener–Hopf type for coefficients of interpolation formulas // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 4/1. – P. 64-73. |
| MLA | Shadimetov, Kh.M., Atamuradova, B.M., Шадиметов, Х.М., and Атамурадова, Б.М. “Discrete system of Wiener–Hopf type for coefficients of interpolation formulas.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 64-73, 2024. https://journals.airi.uz/index.php/pvpm/article/view/49 |
| Chicago | Shadimetov, Kh.M., Atamuradova, B.M., Шадиметов, Х.М., and Атамурадова, Б.М. “Discrete system of Wiener–Hopf type for coefficients of interpolation formulas.” Ҳисоблаш ва амалий математика муаммолари, (4/1), 64-73 (2024). https://journals.airi.uz/index.php/pvpm/article/view/49 |
| Harvard | Shadimetov, Kh.M., Atamuradova, B.M., Шадиметов, Х.М., and Атамурадова, Б.М (2024) ‘Discrete system of Wiener–Hopf type for coefficients of interpolation formulas’, Ҳисоблаш ва амалий математика муаммолари, (4/1), 64-73. https://journals.airi.uz/index.php/pvpm/article/view/49 |
| BibTeX | @article{shadimetovkhm2024,
title = {Discrete system of Wiener–Hopf type for coefficients of interpolation formulas},
author = {Shadimetov, Kh.M. and Atamuradova, B.M. and Шадиметов, Х.М. and Атамурадова, Б.М.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {4/1},
pages = {64-73},
url = {https://journals.airi.uz/index.php/pvpm/article/view/49}
} |
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