On the computation of Gauss quadrature rules for measures with a monomial denominator

Let dμdμ be a nonnegative measure with support on the real axis and let α∈Rα∈R be outside the convex hull of the support. This paper describes a new approach to determining recursion coefficients for Gauss quadrature rules associated with measures of the form dμ̌(x):=dμ(x)/(x−α)2ℓ. The proposed method is based on determining recursion coefficients for a suitable family of orthonormal Laurent polynomials. Numerical examples show this approach to yield higher accuracy than available methods.