The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-06-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/200 |
| _version_ | 1826559044199907328 |
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| author | K. Tukhliev |
| author_facet | K. Tukhliev |
| author_sort | K. Tukhliev |
| collection | DOAJ |
| description | In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown. |
| first_indexed | 2024-04-10T02:25:09Z |
| format | Article |
| id | doaj.art-9ec91148e78e41969a4f9fe05d08be3b |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:54:07Z |
| publishDate | 2013-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-9ec91148e78e41969a4f9fe05d08be3b2025-03-02T12:46:54ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-06-0120312112910.18255/1818-1015-2013-3-121-129194The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and CurvesK. Tukhliev0Khujand State UniversityIn this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown.https://www.mais-journal.ru/jour/article/view/200quadrature formulacurvilinear integralgradienterrornode |
| spellingShingle | K. Tukhliev The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves Моделирование и анализ информационных систем quadrature formula curvilinear integral gradient error node |
| title | The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves |
| title_full | The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves |
| title_fullStr | The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves |
| title_full_unstemmed | The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves |
| title_short | The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves |
| title_sort | optimal quadrature formula of approximate calculation of curvilinear integral of first kind for some classes of functions and curves |
| topic | quadrature formula curvilinear integral gradient error node |
| url | https://www.mais-journal.ru/jour/article/view/200 |
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