an:00641626
Zbl 0806.41018
Ehrich, S.
Gauss-Kronrod quadrature error estimates for analytic functions
EN
Z. Angew. Math. Mech. 74, No. 6, T691-T693 (1994).
00020397
1994
j
41A55 41A80 30E20 33C45 65D32
error bounds; Gauss-Kronrod quadrature; Chebyshev polynomials
Error bounds are proved for the Gauss-Kronrod quadrature formula and analytic functions, using the maximum modulus of the integrand along closed contours in the complex plane, and in particular along circles and ellipses.
Furthermore, the remainder functional is investigated for the first \(\nu\) (for increasing polynomial degree) Chebyshev polynomials of the first and second kind which are not integrated exactly. It is shown, for sufficiently large \(n\) and independent \(\nu\), that these values are negative, and that their absolute values increase with the polynomial degree.
S.Ehrich (Hildesheim)