Modified moments and orthogonal rational functions

In a series of articles 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^k dµ(x) of the measure is generally an ill-conditioned problem. However, in one of these papers 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.status: publishe