Computing rational GaussChebyshev quadrature formulas with complex poles: The algorithm
We provide an algorithm to compute arbitrarily many nodes and weights for rational GaussChebyshev 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) 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.
gausschebyshev quadrature formulas complex poles algorithm orthogonal rational functions numerical integration