On biorthogonal systems of trigonometric functions and quadrature formulas for periodic integrands
Abstract
In this paper, quadrature formulas with an arbitrary number of nodes and exactly integrating trigonometric polynomials up to degree as high as possible are constructed in order to approximate 2?periodic weighted integralsE For this purpose, certain biorthogonal systems of trigonometric functions are introduced and their most relevant properties studied. Some illustrative numerical examples are also given. The paper completes the results previously given by Szeg? in Magy Tud Akad Mat Kut Intez K?zl 8:255?273, 1963 and by some of the authors in Annales Mathematicae et Informaticae 32:5?44, 2005.
 Publication:

Numerical Algorithms
 Pub Date:
 April 2007
 DOI:
 10.1007/s1107500791062
 Bibcode:
 2007NuAlg..44..309C