This paper first demonstrates that an algebraic-hyperbolic spline of eighth order minimizes the norm within a Hilbert space framework. Subsequently, employing Sobolev’s method, which involves constructing a discrete analogue of the differential operator, the spline function is developed. Unknown coefficients of the spline are computed according to predefined smoothness criteria and boundary conditions. As a result, the constructed spline exhibits exceptional smoothness, enhances interpolation accuracy, and precisely reproduces hyperbolic functions, linear polynomials, and constants. The findings indicate that this approach is highly effective for applications requiring smooth interpolation and accurate modeling of physical phenomena. Additionally, incorporating tension parameters enables precise adjustment of the spline’s stiffness or flexibility.
| Mualliflar | Abdullaeva, G.Sh., Абдуллаева, Г.Ш. |
|---|---|
| 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 | 67-82 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.3_67.2025.06 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.3_67.2025.06 · Maqolaning asl sahifasi
Hilbert space, generalized spline, algebraic-hyperbolic spline, convolution, discrete analogue, Гильбертово пространство, обобщенный сплайн, алгебраически-гиперболический сплайн, свёртка, дискретный аналог
| APA | Abdullaeva, G.Sh., & Абдуллаева, Г.Ш. (2025). Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order. Ҳисоблаш ва амалий математика муаммолари, (3), 67-82. https://doi.org/10.71310/pcam.3_67.2025.06 |
|---|---|
| GOST (OAK) | Abdullaeva, G.Sh., Абдуллаева, Г.Ш. Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 3. – P. 67-82. – DOI: 10.71310/pcam.3_67.2025.06. |
| MLA | Abdullaeva, G.Sh., and Абдуллаева, Г.Ш. “Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order.” Ҳисоблаш ва амалий математика муаммолари, (3), 67-82, 2025. https://doi.org/10.71310/pcam.3_67.2025.06 |
| Chicago | Abdullaeva, G.Sh., and Абдуллаева, Г.Ш. “Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order.” Ҳисоблаш ва амалий математика муаммолари, (3), 67-82 (2025). https://doi.org/10.71310/pcam.3_67.2025.06 |
| Harvard | Abdullaeva, G.Sh., and Абдуллаева, Г.Ш (2025) ‘Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order’, Ҳисоблаш ва амалий математика муаммолари, (3), 67-82. https://doi.org/10.71310/pcam.3_67.2025.06 |
| BibTeX | @article{abdullaevagsh2025,
title = {Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order},
author = {Abdullaeva, G.Sh. and Абдуллаева, Г.Ш.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {3},
pages = {67-82},
doi = {10.71310/pcam.3_67.2025.06},
url = {https://doi.org/10.71310/pcam.3_67.2025.06}
} |
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