In spline theory, there are algebraic and variational approaches. In the algebraic approach, splines are considered as some smooth piecewise polynomial functions. In the variational approach, splines are understood as elements of a Hilbert or Banach space that minimize certain functionals. Then, the problems of existence, uniqueness, and convergence of splines and algorithms for constructing them based on the proper properties of splines are studied. In this paper, we study the problem of constructing optimal interpolation formulas 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 optimal interpolation formulas. An explicit expression for the optimal coefficients of an interpolation formula in a Hilbert space is obtained.
| Mualliflar | Boltaev, A.K., Болтаев, А.К. |
|---|---|
| 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 | 2025-01-03 |
| Son | 4/2 |
| Betlar | 33-44 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-08-27 |
Hilbert space, extremal function, error functional, interpolation formula, пространство Гильберта, экстремальная функция, функционал погрешности, интерполяционная формула
| APA | Boltaev, A.K., & Болтаев, А.К. (2025). On one modification of the Sobolev method for approximating a function. Ҳисоблаш ва амалий математика муаммолари, (4/2), 33-44. https://journals.airi.uz/index.php/pvpm/article/view/61 |
|---|---|
| GOST (OAK) | Boltaev, A.K., Болтаев, А.К. On one modification of the Sobolev method for approximating a function // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 33-44. |
| MLA | Boltaev, A.K., and Болтаев, А.К. “On one modification of the Sobolev method for approximating a function.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 33-44, 2025. https://journals.airi.uz/index.php/pvpm/article/view/61 |
| Chicago | Boltaev, A.K., and Болтаев, А.К. “On one modification of the Sobolev method for approximating a function.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 33-44 (2025). https://journals.airi.uz/index.php/pvpm/article/view/61 |
| Harvard | Boltaev, A.K., and Болтаев, А.К (2025) ‘On one modification of the Sobolev method for approximating a function’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 33-44. https://journals.airi.uz/index.php/pvpm/article/view/61 |
| BibTeX | @article{boltaevak2025,
title = {On one modification of the Sobolev method for approximating a function},
author = {Boltaev, A.K. and Болтаев, А.К.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {33-44},
url = {https://journals.airi.uz/index.php/pvpm/article/view/61}
} |
Boshqa maqola uchun iqtibos tayyorlash
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…
Along with classical integration and differentiation, the concepts of fractional integral and fractional differential are widely used in modern mathematics. In this work, we construct an optimal quadrature formula for…
Many mathematical models in science and technology have been reduced to the approximate calculation of singular integrals with Cauchy and Hilbert kernels and the approximate solution of integral equations. In this…
A number of books by I.P. Mysovkikh, A.H. Stroud, V.I. Krylov and H.T. Shulgina are devoted to the approximate calculation of integrals, where the theory of constructing quadrature and cubature formulas is presented and…
The solution of the Cauchy problem for partial differential equations of hyperbolic type J. Hadamard led to singular integrals of a special form. Later they were called integrals in the sense of Hadamard, or Hadamard…
One of the main problems of computational mathematics is the optimization of computational methods in function spaces. Optimization of computational methods has proven itself well in problems of the theory of quadrature…
In this work, using the method of periodization of functions, optimal quadrature formulas of Hermite type will be constructed in spaces where the second derivatives are summable with squares. For this purpose, optimal…
In the world, special attention is paid to the creation of various optimal calculation methods. This article is devoted to the construction of derivative optimal quadrature formulas in the space of differentiable…
This paper presents the construction of an optimal quadrature formula in Sobolev space for integrals with power-logarithmic kernels. Formulas are derived for calculating the coefficients of the optimal quadrature…
One of the classical problems in computational mathematics is to construct an interpolation formulas from a countable set of data. This paper demonstrates the problem of construction of optimal interpolation formulas…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2025-yil arxivi
Fourier integrals of functions appear primarily in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, such as theoretical physics, acoustic…
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…