Kahan's summation algorithm is a method to compute sums:

$$\sum x_i$$

with many terms, without significant error.

I want to do this with very large numbers, and instead of the numbers themselves, I am given their logarithms, $\log x_i$ ($x_i > 0$), and instead of the sum, I want to compute the logarithm of the sum,

$$\log \sum x_i$$

Is there a variation of Kahan's summation for this case?

  • $\begingroup$ Check out this related post. Also worth looking up logsumexp. $\endgroup$
    – GoHokies
    Commented Aug 4, 2016 at 17:37
  • $\begingroup$ @GoHokies I think the logexpsum trick doesn't work well if you have a single very large term and many very small terms. $\endgroup$
    – a06e
    Commented Aug 4, 2016 at 19:22
  • $\begingroup$ scicomp.stackexchange.com/q/24624/988 $\endgroup$
    – a06e
    Commented Aug 4, 2016 at 19:39


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