Research output: Contribution to journal › Article › peer-review
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 journal › Article › peer-review
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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
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187443320&origin=inward&txGid=4340c92f7939e89d650228d2ca068451
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