Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series

Year 2019, Volume: 2 Issue: 4, 168 - 182, 01.12.2019

Gradimir Mılovanovıc

https://doi.org/10.33205/cma.613948

Cited By: 1

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

Supporting Institution

Serbian Academy of Sciences and Arts, Belgrade, Serbia

Project Number

Φ−96.

Thanks

The author was supported in part by the Serbian Academy of Sciences and Arts, Project No. Φ−96.

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