  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 Szego's recursion and the structure of the
matrix representation for the multiplication operator when a general sequence
of orthogonal Laurent polynomials on the unit circle is considered. Secondly,
we analyze the computation of the nodes of the Szego quadrature formulas by
using Hessenberg and five-diagonal matrices. Numerical examples concerning the
family of Rogers-Szego q-polynomials are also analyzed.
