The Gauss-Legendre rule is very popular in the scalar case, which is due in part to its optimality properties.
The first uses the composite trapezoidal rule and the second the Gauss-Legendre rule.
1/p] by the Gauss-Legendre rule for the integral (2.
2, which evidences once more the good performance of the Gauss-Legendre rule.
The Gauss-Legendre rule has proved to be once more the right choice to work out that approximation.
The same problem occurs with Gauss-Legendre rules, because the estimate (4.
6), a possibility for estimating the number of nodes and weights in Gauss-Legendre rules is by requiring that [parallel]G(2m) - G(m)[parallel] satisfies a prescribed tolerance, where G(m) := [[SIGMA].