[Edu-sig] RE: Integration correction

[Kirby Urner]

> But you never use the trapezoidal rule in real life!
> Simpson gives much smaller error for the same amount
> of computation. In fact, it is exact for Kirby's example!
> 
> Henrik

Here's my implementation of Simpson's, except it divides the interval into
2n segments.

 >>> def simpson(f,a,b,n):
 	 h = float(b-a)/(2*n)
	 sum1 = sum(f(a +  2*k   *h) for k in range(1,n))
	 sum2 = sum(f(a + (2*k-1)*h) for k in range(1,n+1))
	 return (h/3)*(f(a)+f(b)) + (2*h/3)*sum1 + (4*h/3)*sum2

 >>> def g(x): return x*x

 >>> simpson(g,0,3,10000)
 8.9999999999999893
 >>> simpson(g,0,3,5000)
 8.9999999999999787

Kirby