Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series

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Constructive Mathematical Analysis
Volume: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 : 39 | Download : 14

Publication Date : 2019-12-01

Article Type : Research Paper

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

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