Optimal quadrature formulas for curvilinear integrals of the first kind Full article
Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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Output data | Year: 2024, Volume: 34, Number: 1, Pages: 80-90 Pages count : 11 DOI: 10.1134/S1055134424010048 | ||||
Tags | quadrature formula, error functional, Sobolev space on a closed curve, embedding constant and function, optimal formula | ||||
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Affiliations |
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Funding (1)
1 | Sobolev Institute of Mathematics | FWNF-2022-0008 |
Abstract:
We consider the problem on optimal quadrature formulas for curvilinear integrals of the first kind that are exact for constant functions. This problem is reduced to the minimization problem 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 asingle point ofthe corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there exists a unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the least possible norm of the error functional in the conjugate space. We show that the tuple of weights of the optimal quadrature formula is a solution of a special nondegenerate system of linear algebraic equations.
Cite:
Vaskevich V.L.
, Turgunov I.
Optimal quadrature formulas for curvilinear integrals of the first kind
Siberian Advances in Mathematics. 2024. V.34. N1. P.80-90. DOI: 10.1134/S1055134424010048 Scopus РИНЦ OpenAlex
Optimal quadrature formulas for curvilinear integrals of the first kind
Siberian Advances in Mathematics. 2024. V.34. N1. P.80-90. DOI: 10.1134/S1055134424010048 Scopus РИНЦ OpenAlex
Original:
Васкевич В.Л.
, Тургунов И.М.
Оптимальные квадратурные формулы для криволинейных интегралов первого рода
Математические труды. 2023. Т.26. №2. С.44-61. DOI: 10.33048/mattrudy.2023.26.203 РИНЦ
Оптимальные квадратурные формулы для криволинейных интегралов первого рода
Математические труды. 2023. Т.26. №2. С.44-61. DOI: 10.33048/mattrudy.2023.26.203 РИНЦ
Dates:
Submitted: | Oct 10, 2023 |
Accepted: | Nov 20, 2023 |
Published print: | Mar 11, 2024 |
Published online: | Mar 11, 2024 |
Identifiers:
Scopus: | 2-s2.0-85187443320 |
Elibrary: | 66332973 |
OpenAlex: | W4392649832 |
Citing:
DB | Citing |
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OpenAlex | 1 |