Editing Covariance (section)

== Numerical computation ==
{{main|Algorithms for calculating variance#Covariance}}
When <math>\operatorname{E}[XY] \approx \operatorname{E}[X]\operatorname{E}[Y]</math>, the equation <math>\operatorname{cov}(X, Y) = \operatorname{E}\left[X Y\right] - \operatorname{E}\left[X\right] \operatorname{E}\left[Y\right]</math> is prone to [[catastrophic cancellation]] if <math>\operatorname{E}\left[X Y\right]</math> and <math>\operatorname{E}\left[X\right] \operatorname{E}\left[Y\right]</math> are not computed exactly and thus should be avoided in computer programs when the data has not been centered before.<ref>[[Donald E. Knuth]] (1998). ''[[The Art of Computer Programming]]'', volume 2: ''Seminumerical Algorithms'', 3rd edn., p. 232. Boston: Addison-Wesley.</ref> [[Algorithms for calculating variance#Covariance|Numerically stable algorithms]] should be preferred in this case.<ref>{{Cite book|last1=Schubert|first1=Erich|last2=Gertz|first2=Michael|title=Proceedings of the 30th International Conference on Scientific and Statistical Database Management |chapter=Numerically stable parallel computation of (Co-)variance |date=2018|chapter-url=http://dl.acm.org/citation.cfm?doid=3221269.3223036|language=en|location=Bozen-Bolzano, Italy|publisher=ACM Press|pages=1–12|doi=10.1145/3221269.3223036|isbn=978-1-4503-6505-5|s2cid=49665540}}</ref>