Asymptotic Error Estimates for the Gauss Quadrature Formula

Asymptotic Error Estimates for the Gauss Quadrature Formula

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...

Error Bounds for Gauss-kronrod Quadrature Formulae

The Gauss-Kronrod quadrature formula Qi//+X is used for a practical estimate of the error R^j of an approximate integration using the Gaussian quadrature formula Q% . Studying an often-used theoretical quality measure, for ߣ* , we prove best presently known bounds for the error constants cs(RTMx)= sup \RlK+x[f]\ ll/(l»lloo<l in the case s = "Sn + 2 + tc , k = L^J LfJ • A comparison with the Ga...

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...

An Error Estimate for Stenger's Quadrature Formula

The basis of this paper is the quadrature formula where q = exp(2A), h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger. An explicit form of the error is given for the case where the integrand has a factor of the form (1 — x)a(\ + x)P, a,ß> -1. Application is made to the evaluation of Cauchy principal value integrals with endpoint singula...