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])).

>A bound should be like this:
>
>   N*eps*max(abs(x))

Ok, more precisely: the sum of two numbers has an error bounded by
2*eps.  So, if you sum them starting from the smaller ones you get what
I wrote above.  If you sum them without sorting them first, which is
the usual way, you get the second expression that you wrote above.

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