Re: Zero or not?

[Miroslaw Kwasniak]

On Mon, Jul 23, 2007 at 12:22:33PM -0400, James Sherman Jr. wrote:
> You asked for the maximum error that could happen.  And if you actually
> compare Francesco's estimate and mine, his is actually lower (I am not
> saying that mine is correct, again I am not an expert).  Also note that what
> Przemek says in his mail.  This really isn't an Octave thing, but floating
> point calculations in general.

... and octave (I assume) does sum in standard, quickest way.

>  Stuff like sorting numbers by absolute value
> can help reduce the error of the operations. 

This is one of methods of improvment in precission. But is very costly :(
I made this method in one program twenty years ago ;)

I can be done in octave in a simplest way:

  [i,i]=sort(abs(x)); s=sum(x(i));

But last year I read one article (title&author forgotten) that there isn't
one method that wins in FP sum precission :(

I've read either that typical FFT gives (statistically) smaller error then
simple DFT - it's an effect of its butterfly summation.