Re: Numerical Differentiation and Integration of Array Data

[syberraith]

Actually I kind of understand what your saying.  I've been playing with this:

n = 1000000
p = 2 * pi;
h = p / (n-1);
g = h / 2;

function y = f ( x ) 
   y = sin( x );
endfunction

t = linspace(0 - g, p + g, n + 1);
a = (f(t+g) - f(t-g))./h;
a = h.*(a(1:end-1) + a(2:end))./2;

u = linspace(0, p, n);
s = sum(a.*h)
s1 = a(end) - a(1)
#plot(u, a,"-1")

The more data points I used the closer s got to s1.  My last try was with
100,000,000 data points.  That overwhelm my machine.  All though at
10,000,000 data points s was x.xxe-13 and s1 was x.xxe-17 so they were on
the way to converging.  Now I have to figure out just how much accuracy do I
need, or can s1 just do by itself. 

I think now the behavior of the c program is OK.  What it is showing is just
s approaching s1.

I also fixed my central difference algorithm so that it minimizes funcion
calls, it now does half the calls it originally did.  Nifty stuff.   

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