Quadrature and orthogonal rational functions
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Orthogonal rational functions and quadrature on an interval
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Ratio asymptotics for orthogonal rational functions on an interval
Journal of Approximation Theory
An interpolation algorithm for orthogonal rational functions
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
A weak-star convergence result for orthogonal rational functions
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Positive rational interpolatory quadrature formulas on the unit circle and the interval
Applied Numerical Mathematics
Full length article: An extension of the associated rational functions on the unit circle
Journal of Approximation Theory
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We provide an algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with complex poles outside [-1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of order O(n). This algorithm is based on the derivation of explicit expressions for the Chebyshev (para-)orthogonal rational functions on [-1, 1] with arbitrary complex poles outside this interval.