Category:Examples of Gaussian Integration Rules

This category contains examples of Gaussian Integration Rule.

A Gaussian integration rule is a numerical integration rule of the form:

$\ds \int_a^b \map w x \map f x \rd x \approx \sum_{i \mathop = 1}^n w_i \map f {x_i}$

where $\map w x$ is a non-negative weight function on the interval $\closedint a b$ such that both:

the $n$ nodes $x_i$

the weights $w_i$

are chosen to make the approximation exact when $f$ is a polynomial of degree less than or equal to $2 n - 1$.

The purpose of the weight function is to build into the rule any special behaviour of the integrand.

Common choices for the weight function are:

$\map w x = 1$ with $\closedint a b = \closedint {-1} 1$

$\map w x = e^x$ with $\closedint a b = \closedint 0 \to$