Standard

The infinite convergence order of near minimal cubature formulas on classes of periodic functions. / Vaskevich, V. L.

в: Complex Variables and Elliptic Equations, Том 66, № 8, 2021, стр. 1213-1224.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Vaskevich, VL 2021, 'The infinite convergence order of near minimal cubature formulas on classes of periodic functions', Complex Variables and Elliptic Equations, Том. 66, № 8, стр. 1213-1224. https://doi.org/10.1080/17476933.2020.1816991

APA

Vaskevich, V. L. (2021). The infinite convergence order of near minimal cubature formulas on classes of periodic functions. Complex Variables and Elliptic Equations, 66(8), 1213-1224. https://doi.org/10.1080/17476933.2020.1816991

Vancouver

Vaskevich VL. The infinite convergence order of near minimal cubature formulas on classes of periodic functions. Complex Variables and Elliptic Equations. 2021;66(8):1213-1224. doi: 10.1080/17476933.2020.1816991

Author

Vaskevich, V. L. / The infinite convergence order of near minimal cubature formulas on classes of periodic functions. в: Complex Variables and Elliptic Equations. 2021 ; Том 66, № 8. стр. 1213-1224.

BibTeX

@article{1a021757b9ab4a5188846195d1607f52,
title = "The infinite convergence order of near minimal cubature formulas on classes of periodic functions",
abstract = "The paper aims to estimate the error of a cubature formula acting on an arbitrary function from the Sobolev space on a multidimensional cube. The norm of the error in the dual space of the Sobolev class is represented as a positive definite quadratic form in the weights of the cubature formula. Given a finite smoothness s of the Sobolev space, we establish a power-law convergence order to zero of error functionals norms for near minimal cubature formulas and cubature formulas of high trigonometric degree. If the smoothness s of the Sobolev space tends to infinity then the power-law convergence order tends to infinity as well.",
keywords = "31B30, 41A44, 41A63, 65D32, Cubature formulas, embedding constant, error functional, extremal function, infinite convergence order, near minimal cubature formulas",
author = "Vaskevich, {V. L.}",
note = "Funding Information: The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0013). Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2021",
doi = "10.1080/17476933.2020.1816991",
language = "English",
volume = "66",
pages = "1213--1224",
journal = "Complex Variables and Elliptic Equations",
issn = "1747-6933",
publisher = "Taylor and Francis Ltd.",
number = "8",

}

RIS

TY - JOUR

T1 - The infinite convergence order of near minimal cubature formulas on classes of periodic functions

AU - Vaskevich, V. L.

N1 - Funding Information: The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0013). Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - The paper aims to estimate the error of a cubature formula acting on an arbitrary function from the Sobolev space on a multidimensional cube. The norm of the error in the dual space of the Sobolev class is represented as a positive definite quadratic form in the weights of the cubature formula. Given a finite smoothness s of the Sobolev space, we establish a power-law convergence order to zero of error functionals norms for near minimal cubature formulas and cubature formulas of high trigonometric degree. If the smoothness s of the Sobolev space tends to infinity then the power-law convergence order tends to infinity as well.

AB - The paper aims to estimate the error of a cubature formula acting on an arbitrary function from the Sobolev space on a multidimensional cube. The norm of the error in the dual space of the Sobolev class is represented as a positive definite quadratic form in the weights of the cubature formula. Given a finite smoothness s of the Sobolev space, we establish a power-law convergence order to zero of error functionals norms for near minimal cubature formulas and cubature formulas of high trigonometric degree. If the smoothness s of the Sobolev space tends to infinity then the power-law convergence order tends to infinity as well.

KW - 31B30

KW - 41A44

KW - 41A63

KW - 65D32

KW - Cubature formulas

KW - embedding constant

KW - error functional

KW - extremal function

KW - infinite convergence order

KW - near minimal cubature formulas

UR - http://www.scopus.com/inward/record.url?scp=85091087934&partnerID=8YFLogxK

U2 - 10.1080/17476933.2020.1816991

DO - 10.1080/17476933.2020.1816991

M3 - Article

AN - SCOPUS:85091087934

VL - 66

SP - 1213

EP - 1224

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 8

ER -

ID: 25417452