Comments on numerically improved Gauss-Legendre quadrature

Abstract 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.