Wikipedia describes this as follows:
An Octave program to sum \(s = x_1 + x_2 + ... + x_n\) is (embedded):
In numerical analysis, the Kahan summation algorithm (also known as compensated summation [1]) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors).Here are a couple of links (postscript document) which argue that this relatively simple method ought to be better known.
An Octave program to sum \(s = x_1 + x_2 + ... + x_n\) is (embedded):
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