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

Deckers, Karl; Van Deun, Joris; Bultheel, Adhemar

doi:10.1090/S0025-5718-07-01982-5

Rational Gauss-Chebyshev quadrature formulas for complex poles outside $[-1,1]$
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by Karl Deckers, Joris Van Deun and Adhemar Bultheel;

Math. Comp. 77 (2008), 967-983

DOI: https://doi.org/10.1090/S0025-5718-07-01982-5

Published electronically: September 28, 2007

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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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