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

Abstract. Let dμ be a nonnegative measure with support on the real axis and let α ∈ 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.