BSU Bulletin. Mathematics, Informatics
Bibliographic description:
A LOWER BOUND FOR THE NORM OF THE PERIODIC ERROR FUNCTIONAL // BSU Bulletin. Mathematics, Informatics. - 2023. №3. . - С. 23-33.
Title:
A LOWER BOUND FOR THE NORM OF THE PERIODIC ERROR FUNCTIONAL
Financing:
Codes:
Annotation:
For the effectiveness of the cubature formula, it is necessary that the norm of the error functional be minimal. To minimize the norm of the functional, a sequence of finite functions is constructed on the basis of averaging the characteristic function of a domain with a piecewise-smooth boundary. In this article, using the properties of an extremal function, we obtain a lower bound for the norm of the error functional for cubature formulas with nodes on parallelepiped lattices in an anisotropic space.
Keywords:
norm of an extremal function, norm of a periodic error functional, asymptotic optimality, lower estimate.
List of references:
Article.pdf