Domain of validity of Szegö quadrature formulas

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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.

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NjÅstad, O., & Santos-León, J. C. (2007). Domain of validity of Szegö quadrature formulas. Journal of Computational and Applied Mathematics, 202(2), 440–449. https://doi.org/10.1016/j.cam.2006.02.039

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