Modified Moments and Orthogonal Rational Functions†

In a series of articles [9, 10, 11] about the numerical computation of orthogonal polynomials on a subset of the real line, Gautschi shows that computing orthogonal polynomials starting from the moments μ_k = ∫ x^kdμ(x) of the measure is generally an ill-conditioned problem. However, in [10] an alternative approach is presented, based on so-called modified moments, which works better in certain situations. In this paper we generalize these results to the computation of orthogonal rational functions and provide a new modified moment algorithm, based on the connection between modified moments and interpolatory quadrature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)