Re: Zero or not?

[Francesco Potorti`]

>>>Ok, that's a start. If I calculate the sum of N numbers, what is the
>>>maximum 'offset' of the numerical result to mathematically correct
>>>result?
>>
>> Not a numerical expert, but the error magnitude should be bounded by
>> eps*sum(abs(x[1:N])).
>
>Are you sure this is what you intended to write? For example:
>
>octave:5> eps
>ans =  2.2204e-16
>octave:6> x = [ 1E5 -1E5 ]; N = length(x);
>octave:7> eps*sum(abs(x(1:N)))
>ans =  4.4409e-11
>
>I just hope (pray) that Octave can do better than this when calculating
>the sum of the values in x (i.e. sum(x))...

How possibly could it?  You get a result of 1e5 and an error of 4e-11.
This is the machine precision, so you cannot get better than this as a
worst case.  Certainly, depending on the precise numbers you sum up you
will generally get smaller errors, or even 0, but the error bound cannot
be smaller.

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