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Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind. / Vaskevich, V. L.; Turgunov, I. M.

In: Siberian Advances in Mathematics, Vol. 34, No. 1, 4, 03.2024, p. 80-90.

Research output: Contribution to journalArticlepeer-review

Harvard

Vaskevich, VL & Turgunov, IM 2024, 'Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind', Siberian Advances in Mathematics, vol. 34, no. 1, 4, pp. 80-90. https://doi.org/10.1134/S1055134424010048

APA

Vancouver

Vaskevich VL, Turgunov IM. Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind. Siberian Advances in Mathematics. 2024 Mar;34(1):80-90. 4. doi: 10.1134/S1055134424010048

Author

Vaskevich, V. L. ; Turgunov, I. M. / Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind. In: Siberian Advances in Mathematics. 2024 ; Vol. 34, No. 1. pp. 80-90.

BibTeX

@article{f675a90ef22449ebbbc9078e5bcd64cf,
title = "Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind",
abstract = "We consider the problem on optimal quadrature formulas for curvilinear integrals ofthe first kind that are exact for constant functions. This problem is reduced to the minimizationproblem for a quadratic form in many variables whose matrix is symmetric and positive definite.We prove that the objective quadratic function attains its minimum at a single point ofthe corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there existsa unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the leastpossible norm of the error functional in the conjugate space. We show that the tuple of weights ofthe optimal quadrature formula is a solution of a special nondegenerate system of linear algebraicequations.",
keywords = "Sobolev space on a closed curve, embedding constant and function, error functional, optimal formula, quadrature formula",
author = "Vaskevich, {V. L.} and Turgunov, {I. M.}",
note = "The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).",
year = "2024",
month = mar,
doi = "10.1134/S1055134424010048",
language = "English",
volume = "34",
pages = "80--90",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "PLEIADES PUBLISHING INC",
number = "1",

}

RIS

TY - JOUR

T1 - Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind

AU - Vaskevich, V. L.

AU - Turgunov, I. M.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).

PY - 2024/3

Y1 - 2024/3

N2 - We consider the problem on optimal quadrature formulas for curvilinear integrals ofthe first kind that are exact for constant functions. This problem is reduced to the minimizationproblem for a quadratic form in many variables whose matrix is symmetric and positive definite.We prove that the objective quadratic function attains its minimum at a single point ofthe corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there existsa unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the leastpossible norm of the error functional in the conjugate space. We show that the tuple of weights ofthe optimal quadrature formula is a solution of a special nondegenerate system of linear algebraicequations.

AB - We consider the problem on optimal quadrature formulas for curvilinear integrals ofthe first kind that are exact for constant functions. This problem is reduced to the minimizationproblem for a quadratic form in many variables whose matrix is symmetric and positive definite.We prove that the objective quadratic function attains its minimum at a single point ofthe corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there existsa unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the leastpossible norm of the error functional in the conjugate space. We show that the tuple of weights ofthe optimal quadrature formula is a solution of a special nondegenerate system of linear algebraicequations.

KW - Sobolev space on a closed curve

KW - embedding constant and function

KW - error functional

KW - optimal formula

KW - quadrature formula

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UR - https://www.elibrary.ru/item.asp?id=67307189

UR - https://www.mendeley.com/catalogue/206e4add-38c5-3b40-91b5-5a44f4a2b428/

U2 - 10.1134/S1055134424010048

DO - 10.1134/S1055134424010048

M3 - Article

VL - 34

SP - 80

EP - 90

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

M1 - 4

ER -

ID: 60535553