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Formulas for Quasi-Interpolation by Integral Quadratic Splines Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2026, Volume: 67, Number: 4, Pages: 774-784 Pages count : 11 DOI: 10.1134/s0037446626040038
Tags integralquadratic spline, integro quadratic spline, mean interpolation, cubic spline, approximation error estimates, superconvergence points, local approximation
Authors Volkov Yu.S. 1 , Zhanlav T. 2 , Mijiddorj R.-O. 3
Affiliations
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

Funding (1)

1 Министерство науки и высшего образования РФ FWNF-2026-0005

Abstract: 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.
Cite: 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
Original: 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
Dates:
Submitted: Nov 25, 2025
Accepted: Apr 5, 2026
Published print: Jul 30, 2026
Published online: Jul 30, 2026
Identifiers:
≡ Web of science: WOS:001837323400005
≡ Scopus: 2-s2.0-105046283547
≡ Elibrary: 91863790
≡ OpenAlex: W7171783738
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