Gaussian quadrature formulae on the unit circle

Authors:
Leyla Daruis;Pablo González-Vera;Francisco Marcellán
Affiliations:
Department of Mathematical Analysis, La Laguna University, Tenerife, Canary Islands, Spain;-;-
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

Citing 4
Cited 4

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Abstract

Let µ be a probability measure on [0, 2π]. In this paper we shall be concerned with the estimation of integrals of the form Iµ(f)= (1/2π) ∫02π f(eiθ)dµ(θ). For this purpose we will construct quadrature formulae which are exact in a certain linear subspace of Laurent polynomials. The zeros of Szegö polynomials are chosen as nodes of the corresponding quadratures. We will study this quadrature formula in terms of error expressions and convergence, as well as, its relation with certain two-point Padé approximants for the Herglotz-Riesz transform of µ. Furthermore, a comparison with the so-called Szegö quadrature formulae is presented through some illustrative numerical examples.