The Computer Journal · 1961 · 67 citations · 0 references
ComputingComputer ScienceComputational PhysicsMethod ValidationScientific ComputingConvergence AnalysisError EstimationNumerical AnalysisNumerical ConvergenceNumerical IntegrationConvergenceGaussian QuadratureQuadrature RulesQuadrature Theory
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.