Back to Search
Start Over
Coefficients of optimal quadrature formulas in the space of differentiable functions.
- Source :
-
AIP Conference Proceedings . 2024, Vol. 3004 Issue 1, p1-11. 11p. - Publication Year :
- 2024
-
Abstract
- In this paper, we consider the construction of an optimal lattice quadrature formula in the space W 2 (m) (0, 1). Further, finding the extremal function of the error functional of quadrature formulas, by virtue of the Riesz theorem on the general form of a linear continuous functional, is reduced to solving a boundary value problem for ordinary differential equations. Solving this boundary value problem, we obtain an explicit expression for the extremal function of the error functional of quadrature formulas. In addition, by virtue of the Riesz theorem, the square of the norm of the error functional is explicitly calculated and an analytical expression is obtained for the optimal coefficients of the quadrature formulas at m = 2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 3004
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 175958292
- Full Text :
- https://doi.org/10.1063/5.0200106