Domain of validity of Szegö quadrature formulas

Abstract

As is well known, the n-point Szegö quadrature formula integrates correctly any Laurent polynomial in the subspace span{1 / zn - 1, ..., 1 / z, 1, z, ..., zn - 1 }. In this paper we enlarge this subspace. We prove that a set of 2 n linearly independent Laurent polynomials are integrated correctly. The obtained result is used for the construction of Szegö quadrature formulas. Illustrative examples are given. © 2006 Elsevier B.V. All rights reserved.