Comments on numerically improved Gauss–Legendre quadrature

We show that numerically improved n-point Gauss–Legendre (NIGL) quadrature is interpolatory, has positive weights and is convergent as n → ∞. We derive expressions for both the analytical error and the numerical error. We demonstrate that, for n = 2 and n = 3, NIGL quadrature has weights and abscissae very similar to that of standard Gauss–Legendre quadrature.