Orthogonal Laurent polynomials corresponding to certain strong Stieltjes distributions with applications to numerical quadratures

Díaz-Mendoza, C.; González-Vera, P.; Paiz, M.; Rodríguez, F.

doi:10.1090/S0025-5718-05-01781-3

Orthogonal Laurent polynomials corresponding to certain strong Stieltjes distributions with applications to numerical quadratures
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by C. Díaz-Mendoza, P. González-Vera, M. Jiménez Paiz and F. Cala Rodríguez;

Math. Comp. 75 (2006), 281-305

DOI: https://doi.org/10.1090/S0025-5718-05-01781-3

Published electronically: September 9, 2005

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Abstract:

In this paper we shall be mainly concerned with sequences of orthogonal Laurent polynomials associated with a class of strong Stieltjes distributions introduced by A.S. Ranga. Algebraic properties of certain quadratures formulae exactly integrating Laurent polynomials along with an application to estimate weighted integrals on $[-1,1]$ with nearby singularities are given. Finally, numerical examples involving interpolatory rules whose nodes are zeros of orthogonal Laurent polynomials are also presented.

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