Catastrophic Cancellation

[Rob Mahurin]

That's a great example! I love the distinction between the one-bit  
and the continuous errors.

In Octave, you don't need the loop, though:

	octave-3.0.1> x = 1e-7*linspace(-1,1,1e3);
	octave-3.0.1> y = [ 	(1-cos(x))./x.^2;
				1./x.^2 - cos(x)./x.^2;
				(1 - x.^2/12)/2;
			];
	octave-3.0.1> plot(x,y,'o-');

Cheers,
Rob

On Jul 1, 2008, at 5:50 PM, A. Kalten wrote:

> Just to spread some awareness of the pitfalls of floating point
> calculations, I urge everyone to try this simple test.  At the
> octave prompt enter:
>
> x=-4e-8:1e-10:4e-8;
> for i=1:length(x)
> y(i)=(1-cos(x(i)))/x(i)/x(i);
> endfor
> plot(x,y)
>
> Hopefully, the results should surprise, or even shock, you.
>
> Also try rewriting the above function as: y(i)=1/x(i)/x(i)-cos(x 
> (i))/x(i)/x(i)
>
> For more info, the link is here:
>
> http://www.cs.princeton.edu/introcs/lectures/9scientific.pdf
>
> AK
>
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-- 
Rob Mahurin
Dept. of Physics & Astronomy
University of Tennessee 	phone: 865 207 2594
Knoxville, TN 37996     	email: rob at utk.edu