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


Authors: C. Díaz-Mendoza, P. González-Vera, M. Jiménez Paiz and F. Cala Rodríguez
Journal: Math. Comp. 75 (2006), 281-305
MSC (2000): Primary 41A21, 30E05
DOI: https://doi.org/10.1090/S0025-5718-05-01781-3
Published electronically: September 9, 2005
MathSciNet review: 2176400
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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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Additional Information

C. Díaz-Mendoza
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: cjdiaz@ull.es

P. González-Vera
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: pglez@ull.es

M. Jiménez Paiz
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: mjimenez@ull.es

F. Cala Rodríguez
Affiliation: Centro de Docencia Superior en Ciencias Básicas, Campus Puerto Montt, Universidad Austral de Chile, Puerto Montt, Chile
Email: fcala@uach.cl

DOI: https://doi.org/10.1090/S0025-5718-05-01781-3
Keywords: Strong Stieltjes distributions, orthogonal Laurent polynomials, quadrature formulas, Stieltjes transform, two-point Pad\'e approximants
Received by editor(s): November 4, 2003
Received by editor(s) in revised form: August 2, 2004
Published electronically: September 9, 2005
Additional Notes: The first three authors were partially supported by the Scientific Research Projects of the Ministerio de Ciencia y Tecnología and Comunidad Autónoma de Canarias under contracts BFM2001-3411 and PI 2002/136, respectively
The work of the fourth author was done during a visit to the Departamento de Análisis Matemático in Universidad de La Laguna (Canary Islands, Spain).
Article copyright: © Copyright 2005 American Mathematical Society

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