Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series
A summation/integration method for fast summing trigonometric series is presented. The basic idea in this method is to transform the series to an integral with respect to some weight function on \RR_+ and then to approximate such an integral by the appropriate quadrature formulas of Gaussian type. The construction of these quadrature rules, as well as the corresponding orthogonal polynomials on \RR_+ are also considered. Finally, in order to illustrate the efficiency of the presented summation/integration method two numerical examples are included.
Constructive Mathematical Analysis