Miodrag M. Spalevic

Aleksandar V. Pejcev, Miodrag M. Spalevic

Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.

Ramon Orive, Aleksandar V. Pejcev, Miodrag M. Spalevic

In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of anyone of the four Chebyshev weights, considered by Gautschi and Li in \cite{gauli}. As it is well known, in the case of analytic integrands, the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel, as it is often considered, on elliptic contours with foci at the points $\mp 1$ and such that the sum of semi-axes is $ρ>1$, of the mentioned quadrature formulas, and derive some error bounds for them. In addition, we obtain, for the first time as far as we know, a result about the behavior of the modulus of the corresponding kernels on those ellipses in some cases. Numerical examples checking the accuracy of such error bounds are included.