Construction of Optimal Quadrature Formulas Exact for Exponentional-trigonometric Functions by Sobolev’s Method

• Published in: Acta mathematica Sinica. English series Vol. 37; no. 7; pp. 1066 - 1088
• Main Authors: Boltaev, Aziz, Hayotov, Abdullo, Shadimetov, Kholmat
• Format: Journal Article
• Language: English
• Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.07.2021; Springer Nature B.V
• Subjects: Differential equations; Lagrange multiplier; Linear equations; Mathematical analysis; Mathematics; Mathematics and Statistics; Operators (mathematics); Quadratures; Trigonometric functions; discrete analogue; 65D30; 65D32; optimal coefficients; the error functional; The extremal function; 41A15; Sobolev’s method; 41A05

The paper studies Sard’s problem on construction of optimal quadrature formulas in the space W 2 ( m ,0) by Sobolev’s method. This problem consists of two parts: first calculating the norm of the error functional and then finding the minimum of this norm by coefficients of quadrature formulas. Here...