Glossary

Degree of precision

The highest polynomial degree that a quadrature formula integrates exactly.

Definition

A formula has degree of precision $m$ if it integrates every polynomial of degree $\le m$ exactly and fails for some polynomial of degree $m+1$ . Simpson reaches degree 3 with only three nodes; Gauss-Legendre with $n$ nodes reaches $2n-1$ , the maximum possible.

How it is used

You check it by integrating the monomials $1, x, x^2,\dots$ , and it is the quick way to compare formulas before looking at error constants.