- Constructive Mathematical Analysis
- Vol: 2 Issue: 4
- Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series
Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series
Authors : Gradimir Milovanovic
Pages : 168-182
Doi:10.33205/cma.613948
View : 11 | Download : 6
Publication Date : 2019-12-01
Article Type : Research
Abstract :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.Keywords : Summation, trigonometric series, Gaussian quadrature rule, orthogonal polynomial, three-term recurrence relation, weight function, Laplace transformation