Numerical Analysis: Two-dimensional Integration: Radon's Formula

• December 20th 2008, 10:44 AM
dx27
Numerical Analysis: Two-dimensional Integration: Radon's Formula
Hi!

$
\int _{-1}^1\int _{-1}^1f(x,y)dxdy
$

$
\approx\frac{5}{9}[f(r,s)+f(r,-s)+f(-r,s)+f(-r,-s)]+\frac{20}{63}[f(0,t)+f(0,-t)]+\frac{8}{7}f(0,0)
$
,
where $r=\sqrt{3/5}, s=\sqrt{1/3}, t=\sqrt{14/15}$.

I think it's called Radon's formula for 7 points. I'd like to know more about this approximation, especially how it's derived and if there's more general formula.

If anyone knows anything about it I'd be grateful. I've been trying to google it, but with no success (I don't know if it has different names).

Thank you!