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

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

2006-06-16

arxiv.org/abs/math/0606388v1

Mathematics

Numerical Analysis

39 pages, 2 figures, 10 tables

Scientific paper

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.

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