A matrix approach to the computation of quadrature formulas on the unit circle

In this paper we consider a general sequence of orthogonal Laurent polynomials on the unit circle and we first study the equivalences between recurrences for such families and Szegö's recursion and the structure of the matrix representation for the multiplication operator in Λ when a general sequence of orthogonal Laurent polynomials on the unit circle is considered. Secondly, we analyze the computation of the nodes of the Szegö quadrature formulas by using Hessenberg and five-diagonal matrices. Numerical examples concerning the family of Rogers–Szegö q-polynomials are also analyzed.