A quadrature integration rule is a method of numerical approximation of the definite integral of a function, particularly as a weighted sum of function values at quadrature points within the domain of integration:
In one dimension, on the domain (-1, 1), some low order polynomials can be integrated as follows:
Number of points | Quadrature weights | Quadrature points |
---|---|---|
1 | 2 | 0 |
2 | 1, 1 | -1/√3, 1/√3 |
3 | 5/9, 8/9, 5/9 | -√(3/5), 0, √(3/5) |