Rates of Convergence of Gaussian Quadrature for Singular Integrands

摘要

The rates of convergence (or divergence) or Gaussian quadrature on functions with an algebraic or logarithmic singularity inside, or at an endpoint of, the interval of integration is obtained. Upper and lower bounds for the error in Gaussian integration were obtained, using a generalized Markov-Stieltjes inequality. These estimates lead to asymptotic results for the error in Gaussian integration whether the singularity is ignored or avoided.