## Gaussian Quadrature

Anyone care to explain the concept of gaussian quatrature? I've tried some websites but they're a little over my head. An example would be appreciated, thanks!

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 i think it just means solving using integration.
 Well I know its a system of Legendre polynomials used to approximate functions, but I'm not sure of how to actually do it, if any one knows I'd appreciate an explination.

Recognitions:
Gold Member

Gaussian integration involves Hermite polynomials, Legendre polynomials, Laugarre polynomials amongst others. In general, the integral of a function $$\int f(x) g dx$$ where $$g$$ is a weighting function, which can be $$e^{-x}, e^{-x^2/2}$$ etc.... can be written as $$\sum_{i} f(x_i) w_i$$. The $$x_i$$ are the roots of the polynomials you wsh to use to fit and $$w$$ are weighting functions at those roots.