Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

Abstract

In this paper we consider interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree of exactness. Our approach is based on a procedure given by Ghizzeti and Ossicini (Quadrature formulae, AcademieVerlag, Berlin, 1970). We introduce and consider the so-called σ -orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Also, some numerical examples are included.