Error bounds and estimates for gauss-turan quadrature formulae of analytic functions

Abstract

We study the error of Gauss-Turan quadrature formulae when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for arbitrary weight functions. A comparison is made with the exact error, and a number of numerical examples for arbitrary weight functions are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with the other effective error bounds for some special weight functions appearing in the literature. Asymptotic error estimates when the number of nodes in the quadrature increases are presented. A couple of numerical examples which show their efficiency are included.