V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Estimates for the remainders of certain quadrature formulas”, Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 4,Pages <nobr>497

Estimates for the remainders of certain quadrature formulas

V. A. Abilov^a, F. V. Abilova^b, M. K. Kerimov^c

^a Dagestan State University, Makhachkala, Russia
^b Dagestan State Technical University, Makhachkala, Russia
^c Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia

Abstract: Estimates of the remainders of certain quadrature formulas are obtained, in particular, of quadrature formulas with nodes that are the zeros of Chebyshev polynomials of the first kind in classes of differentiable functions characterized by a generalized modulus of continuity.

Key words: weight function, shift operator, generalized modulus of continuity, $N$-width, Chebyshevtype quadrature formula.

UDC: 519.644.7

Received: 13.07.2017

DOI: 10.7868/S0044466918040014