Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series

Abstract

A summation/integration method for fast summing trigonometric series is presented. The basicidea in this method is to transform the series to an integral with respect to some weight function on R+ and thento approximate such an integral by the appropriate quadrature formulas of Gaussian type. The construction ofthese quadrature rules, as well as the corresponding orthogonal polynomials on R+, are also considered. Finally,in order to illustrate the efficiency of the presented summation/integration method two numerical examples areincluded.