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

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

In: Complex Variables and Elliptic Equations, Vol. 66, No. 8, 2021, p. 1213-1224.

Research output: Contribution to journal › Article › peer-review

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