New symmetric interpolatory quadrature formulas

We introduce two families of symmetric, interpolatory integration formulas on the interval [-1,1]. These formulas, related to the class of recursive monotone stable (RMS) formulas, allow the application of higher order or compound rules with an efficient reuse of computed function values. One family (SM) uses function values computed outside the integration interval, the other one (HR) uses derivative data. These formulas are evaluated using a practical test based on a tecnique for comparing automatic quadrature routines introduced by Lyness and Kaganove and improved by the authors.