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Formulas for Quasi-Interpolation by Integral Quadratic Splines Научная публикация

Журнал

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Вых. Данные

Год: 2026, Том: 67, Номер: 4, Страницы: 774-784 Страниц : 11 DOI: 10.1134/s0037446626040038

Ключевые слова

integralquadratic spline, integro quadratic spline, mean interpolation, cubic spline, approximation error estimates, superconvergence points, local approximation

Авторы

Volkov Yu.S. ¹ , Zhanlav T. ² , Mijiddorj R.-O. ³

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia
3	Mongolian National University of Education, Ulaanbaatar, Mongolia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0005

We consider the problem of approximating a function by integral quadratic splines, also known as integro quadratic splines, from the known integral averages over the mesh intervals. It is shown that, in the mean interpolation problem, an integral quadratic spline can be defined in terms of an interpolating cubic spline. Since interpolating cubic splines have been studied quite well, some of their properties can be transferred to integral quadratic splines. We propose formulas for quasi-interpolation by integral quadratic splines. The problem of local approximation by integral splines is considered for the first time on an arbitrary nonuniform mesh. On a uniform mesh, we find all superconvergence points for mean interpolation and quasi-interpolation, i.e., the points at which the approximation order increases. It is shown that the jump (the ratio of the magnitude of the discontinuity to the mesh size) of the second derivative of both splines approximates the third derivative with fourth-order accuracy.

Volkov Y.S. , Zhanlav T. , Mijiddorj R.-O.
Formulas for Quasi-Interpolation by Integral Quadratic Splines
Siberian Mathematical Journal. 2026. V.67. N4. P.774-784. DOI: 10.1134/s0037446626040038 WOS Scopus РИНЦ OpenAlex

Волков Ю.С. , Жанлав Т. , Мижиддорж Р.-О.
Формулы квазиинтерполяции интегральными квадратическими сплайнами
Сибирский математический журнал. 2026. Т.67. №4. С.603-615. DOI: 10.33048/smzh.2026.67.403 РИНЦ

Поступила в редакцию:	25 нояб. 2025 г.
Принята к публикации:	5 апр. 2026 г.
Опубликована в печати:	30 июл. 2026 г.
Опубликована online:	30 июл. 2026 г.

≡ Web of science:	WOS:001837323400005
≡ Scopus:	2-s2.0-105046283547
≡ РИНЦ:	91863790
≡ OpenAlex:	W7171783738