Talk:Loss of significance
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The page reads:
'Examples of ill-conditioned calculations are:
- Subtracting two almost equal numbers
- Division by almost zero
In these ill-conditioned calculations you get errors which tend to blow up dramatically. '
Division by a small non-zero number does not result in loss of significance. It may (depending on the numerator) cause numerical overflow, as may multiplication, addition, or subtraction. This is a very different and separate problem from loss of significance.
Subtraction of almost equal numbers is the sole source of loss of significance.
The formula given for loss of significance gives undefined results for x < y. Is "assuming x > y" missed out, or should it be abs(1 - y / x)?
I think this page is a good place to mention cathastropic cancelation. This is already mentioned once by someone else but might have been unclear and incomplete. 18:44, 13 March 2007 Ehdr (Talk | contribs) m (Mentioned "cancellation") Citations maybe usable from "What Every Computer Scientist Should Know About Floating-Point Arithmetic", by David Goldberg
84.41.135.110 17:25, 4 July 2007 (UTC)
