Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series

Gradimir Milovanovic
2019 Constructive Mathematical Analysis  
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 R + 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 R + , are also considered. Finally, in order to illustrate the efficiency of the presented
more » ... sented summation/integration method two numerical examples are included.
doi:10.33205/cma.613948 fatcat:ope7fzgqbzcspfw5tfjenzrfwa