Optimal quadrature formulas for curvilinear integrals of the first kind | Sciact - Система учета научной деятельности ИМ СО РАН

Optimal quadrature formulas for curvilinear integrals of the first kind Научная публикация

Журнал

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Вых. Данные

Год: 2024, Том: 34, Номер: 1, Страницы: 80-90 Страниц : 11 DOI: 10.1134/S1055134424010048

Ключевые слова

quadrature formula, error functional, Sobolev space on a closed curve, embedding constant and function, optimal formula

Авторы

Vaskevich V.L. ^1,2 , Turgunov I. ²

Организации

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0008

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.

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

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

Поступила в редакцию:	10 окт. 2023 г.
Принята к публикации:	20 нояб. 2023 г.
Опубликована в печати:	11 мар. 2024 г.
Опубликована online:	11 мар. 2024 г.

Scopus:	2-s2.0-85187443320
РИНЦ:	66332973
OpenAlex:	W4392649832

БД	Цитирований
OpenAlex	1