Finding the Extremum of the Error Functional in the Space of Periodic Functions
DOI:
https://doi.org/10.71310/pcam.1_71.2026.08Keywords:
space, extremal function, generalized function, operator, optimal quadrature formula, error functionalAbstract
The problem of constructing optimal quadrature formulas for approximate calculation of definite integrals and approximation of functions is one of the important problems of computational mathematics. These problems have been studied by many mathematicians and there are several methods for constructing optimal quadrature formulas. One of these methods is the method proposed by S.L. Sobolev with the concept of an extremal function of the error functional. This article is devoted to finding the main elements necessary for the process of constructing an optimal quadrature formula for real-valued periodic functions in a Hilbert space. The quadrature formula under consideration is a form of the norm of the error functional for obtaining the upper bound of the error. In turn, to find the form of the norm of the error functional, we need an extremal function corresponding to the error functional. This work is aimed at finding the extremal function of the error functional.
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