How does Gaussian quadrature work?

[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 anyone knows I'd appreciate an explanation.

 

[Dr Transport]

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.


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

www.nr.com