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Rational Gauss-Chebyshev quadrature formulas for complex poles outside $ [-1,1]$


Authors: Karl Deckers, Joris Van Deun and Adhemar Bultheel
Journal: Math. Comp. 77 (2008), 967-983
MSC (2000): Primary 42C05, 65D32
DOI: https://doi.org/10.1090/S0025-5718-07-01982-5
Published electronically: September 28, 2007
MathSciNet review: 2373187
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Abstract: In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside $ [-1,1]$ to arbitrary complex poles outside $ [-1,1]$. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside $ [-1,1]$.


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Additional Information

Karl Deckers
Affiliation: Department of Computer Science, K. U. Leuven, B-3001 Heverlee, Belgium
Email: karl.deckers@cs.kuleuven.be

Joris Van Deun
Affiliation: Department of Computer Science, K. U. Leuven, B-3001 Heverlee, Belgium
Address at time of publication: Department of Mathematics and Computer Science, Universiteit Antwerpen, B-2020 Antwerpen, Belgium
Email: joris.vandeun@ua.ac.be

Adhemar Bultheel
Affiliation: Department of Computer Science, K. U. Leuven, B-3001 Heverlee, Belgium
Email: adhemar.bultheel@cs.kuleuven.be

DOI: https://doi.org/10.1090/S0025-5718-07-01982-5
Keywords: Quadrature formulas, orthogonal rational functions
Received by editor(s): February 9, 2006
Published electronically: September 28, 2007
Additional Notes: The work of the first two authors was partially supported by the Fund for Scientific Research (FWO), projects ‘CORFU: Constructive study of orthogonal functions’, grant #G.0184.02 and, ‘RAM: Rational modelling: optimal conditioning and stable algorithms’, grant #G.0423.05, and by the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with the authors.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.