Open AccessOn optimal interval quadrature formulae on classes of differentiable periodic functions
Author(s) -
В. Ф. Бабенко,
Dmytro Skorokhodov
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/240703
Subject(s) - mathematics , quadrature (astronomy) , equidistant , differentiable function , invariant (physics) , interval (graph theory) , class (philosophy) , periodic function , mathematical analysis , combinatorics , pure mathematics , discrete mathematics , geometry , physics , artificial intelligence , computer science , optics , mathematical physics
We solved the problem about the best interval quadrature formula on the class $W^r F$ of differentiable periodic functions with arbitrary permutation-invariant set $F$ of derivatives of order $r$. We proved that the formula with equal coefficients and $n$ node intervals, which have equidistant middle points, is the best on given class.