ERROR ESTIMATES OF GAUSS-TURAN QUADRATURES

Abstract

A survey of our recent results on the error of Gauss-Tur´an quadrature formulae for functions which are analytic on a neighborhood of the set of integration is given. In particular, 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 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. Asymptotic error estimates when the number of nodes in the quadrature increases are presented. A couple of numerical examples are included.