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

 

Rational Szegő quadratures associated with Chebyshev weight functions


Authors: Adhemar Bultheel, Ruymán Cruz-Barroso, Karl Deckers and Pablo González-Vera
Journal: Math. Comp. 78 (2009), 1031-1059
MSC (2000): Primary 42C05, 65D32
Published electronically: December 9, 2008
MathSciNet review: 2476569
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Abstract: In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experiments are finally presented.


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Additional Information

Adhemar Bultheel
Affiliation: Department of Computer Science, K.U.Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium.
Email: Adhemar.Bultheel@cs.kuleuven.be

Ruymán Cruz-Barroso
Affiliation: Department of Computer Science, K.U.Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium.
Address at time of publication: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: szegoquadrature@hotmail.com

Karl Deckers
Affiliation: Department of Computer Science, K.U.Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium.
Email: Karl.Deckers@cs.kuleuven.be

Pablo González-Vera
Affiliation: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Canary Islands, Spain
Email: pglez@ull.es

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02208-4
PII: S 0025-5718(08)02208-4
Keywords: Rational Szeg\H {o} quadrature formulas, Szeg\H {o} quadrature formulas, orthogonal rational functions, Chebyshev weight functions.
Received by editor(s): May 5, 2008
Published electronically: December 9, 2008
Additional Notes: The work of the first three authors was partially supported by the Fund of Scientific Research (FWO), project “RAM: Rational modelling: optimal conditioning and stable algorithms”, grant #G.0423.05 and the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with the authors.
The work of the last author was partially supported by the research project MTM 2005-08571 of the Spanish Government.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.