It is interesting (if I am reading this correctly) that the answer depends on the order you add the numbers up in.
------------Original Message------------
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "'Barton Willis'" <willisb at unk.edu>
Cc: "'Maxima List'" <maxima at math.utexas.edu>
Date: Wed, May-7-2008 3:06 PM
Subject: Re: [Maxima] Big float Round off errors
There is a brief summary of some of the many proposed ways of accurate
summation here:
http://hpcrd.lbl.gov/SCG/ocean/NRS/ECMWF/img11.htm
There is a long history of this problem, and though you may think that this
should yield to off-the-top-of-the-head analysis and is trivial, you might
be surprised by the different results by (for example)
Donald Knuth, William Kahan, David Bailey and others.
RJF
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