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 natural spline functions in a Hilbert space. Here, using the Sobolev method, an algorithm is given for solving a system of linear algebraic equations for the coefficients of the natural spline functions. For ???? = 2, explicit expressions for the optimal coefficients of the natural spline function in the Hilbert space ????(2,0) are obtained.
| Mualliflar | Boltaev, A.K., Pardaeva, O.F., Болтаев, А.К., Пардаева, О.Ф. |
|---|---|
| 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 | 2025-07-27 |
| Son | 3 |
| Betlar | 97-106 |
| Til | Ingliz |
| DOI | 10.71310/pcam.3_67.2025.08 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.3_67.2025.08 · Maqolaning asl sahifasi
Hilbert space, extremal function, error functional, spline function, пространство Гильберта, экстремальная функция, функционал погрешности, сплайн функция
| APA | Boltaev, A.K., Pardaeva, O.F., Болтаев, А.К., & Пардаева, О.Ф. (2025). On an Interpolation of a Function by Natural Splines. Ҳисоблаш ва амалий математика муаммолари, (3), 97-106. https://doi.org/10.71310/pcam.3_67.2025.08 |
|---|---|
| GOST (OAK) | Boltaev, A.K. va b. On an Interpolation of a Function by Natural Splines // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 3. – P. 97-106. – DOI: 10.71310/pcam.3_67.2025.08. |
| MLA | Boltaev, A.K., Pardaeva, O.F., Болтаев, А.К., and Пардаева, О.Ф. “On an Interpolation of a Function by Natural Splines.” Ҳисоблаш ва амалий математика муаммолари, (3), 97-106, 2025. https://doi.org/10.71310/pcam.3_67.2025.08 |
| Chicago | Boltaev, A.K., Pardaeva, O.F., Болтаев, А.К., and Пардаева, О.Ф. “On an Interpolation of a Function by Natural Splines.” Ҳисоблаш ва амалий математика муаммолари, (3), 97-106 (2025). https://doi.org/10.71310/pcam.3_67.2025.08 |
| Harvard | Boltaev, A.K., Pardaeva, O.F., Болтаев, А.К., and Пардаева, О.Ф (2025) ‘On an Interpolation of a Function by Natural Splines’, Ҳисоблаш ва амалий математика муаммолари, (3), 97-106. https://doi.org/10.71310/pcam.3_67.2025.08 |
| BibTeX | @article{boltaevak2025,
title = {On an Interpolation of a Function by Natural Splines},
author = {Boltaev, A.K. and Pardaeva, O.F. and Болтаев, А.К. and Пардаева, О.Ф.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {3},
pages = {97-106},
doi = {10.71310/pcam.3_67.2025.08},
url = {https://doi.org/10.71310/pcam.3_67.2025.08}
} |
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