Gaussian Quadrature`

skiboka33

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!

robousy

i think it just means solving using integration.

skiboka33

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.

Dr Transport

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


Look at the Numerical Recipies web site and they explain it very well.

www.nr.com