Anti-Gaussian quadrature rule for trigonometric polynomials

Abstract

In this paper, anti-Gaussian quadrature rules for trigonometric polynomials are introduced. Special attention is paid to an even weight function on $[-\pi,\pi)$.
 The main properties of such quadrature rules are proved and  a numerical method for their construction is presented. That method is based on relations between nodes and weights of the quadrature rule for trigonometric polynomials and the quadrature rule for algebraic polynomials.  Some numerical examples are included. Also, we compare our method with other available methods.