The error bounds of Gauss-Lobatto quadratures for weights of Bernstein-Szegö type

Abstract

In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szeg? weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form ?(t) = 1-4?/(1+?)2 t2, where t ?(-1,1) and ? ? (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.