Generalized averaged Szegő quadrature rules

Szegő quadrature rules are commonly applied to integrate periodic functions on the unit circle in the complex plane. However, often it is difficult to determine the quadrature error. Recently, Spalević introduced generalized averaged Gauss quadrature rules for estimating the quadrature error obtained when applying Gauss quadrature over an interval on the real axis. We describe analogous quadrature rules for the unit circle that often yield higher accuracy than Szegő rules using the same moment information and may be used to estimate the error in Szegő quadrature rules.