Asymptotic estimates for the error of the Gauss-Legendre quadrature formula

Asymptotic Error Estimates for the Gauss Quadrature Formula

Estimates of the error in Gauss-Legendre quadrature for double integrals

Error estimates are a very important aspect of numerical integration. It is desirable to know what level of truncation error might be expected for a given number of integration points. Here, we determine estimates for the truncation error when Gauss-Legendre quadrature is applied to the numerical evaluation of two dimensional integrals which arise in the boundary element method. Two examples ar...

Error of the Newton-Cotes and Gauss-Legendre Quadrature Formulas

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

Error Estimates for Gauss Quadrature Formulas for Analytic Functions

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules

We show that the weights of extended Gauss-Legendre quadrature rules are all positive.