Quadrature Rules With an Even Number of Multiple Nodes and a Maximal Trigonometric Degree of Exactness

Abstract

This paper is devoted to the interpolatory quadrature rules with an even number of multiple nodes, which have the maximal trigonometric degree of exactness. For  constructing of such quadrature rules we introduce and consider the so--called $s-$ and $\sigma-$orthogonal trigonometric polynomials. We present a numerical method  for construction of mentioned quadrature rules. Some numerical examples are also included.