Convergence Properties of Gaussian Quadrature Formulae

1961/04/01 by W. Barrett · 3 citations
Physics and Astronomy · Mathematics · Earth and Planetary Sciences · #Electromagnetic Scattering and Analysis #Iterative Methods for Nonlinear Equations #Geophysics and Gravity Measurements

paper · pdf · doi:10.1093/comjnl/3.4.272

Abstract

An expression is found for the remainder of any Gaussian quadrature formula as a contour integral, and is then used to obtain estimates of the error in certain cases. Numerical examples are given comparing the actual and estimated errors. A method of constructing more general quadrature formulae is described, and two examples are given of formulae so constructed.

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• Is Gauss Quadrature Better than Clenshaw–Curtis?
• A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders
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