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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadratures and Padé approximation


Authors: C. Díaz-Mendoza, P. González-Vera and M. Jiménez-Paiz
Journal: Math. Comp. 74 (2005), 1843-1870
MSC (2000): Primary 42C05, 41A55
Published electronically: June 7, 2005
MathSciNet review: 2164100
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Abstract: Starting from a strong Stieltjes distribution $\phi$, general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution $\phi$ and two-point Padé approximants to the Stieltjes transform of $\phi$ is revisited. Finally, illustrative numerical examples are discussed.


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Additional Information

C. Díaz-Mendoza
Affiliation: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: cjdiaz@ull.es

P. González-Vera
Affiliation: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Canary Islands, Spain

M. Jiménez-Paiz
Affiliation: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Canary Islands, Spain

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01763-1
PII: S 0025-5718(05)01763-1
Keywords: Strong Stieltjes distributions, orthogonal Laurent polynomials, quadrature formulas, Stieltjes transform, two-point Pad\'e approximants.
Received by editor(s): May 5, 2003
Received by editor(s) in revised form: May 4, 2004
Published electronically: June 7, 2005
Additional Notes: This work was 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.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.