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I need some informations about algorithms to solve the problem of catastrophic cancellation, or in general to calculate mean and variance of a data stream. For example about Donald Knuth's algorithm or, also, about new algorithms or methods to solve the same problem.

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    $\begingroup$ Could you sketch what this problem is? Also "Donald Knuth's algorithm" is at about the same level of specificity as "that paper by Erdös". $\endgroup$ Mar 7, 2014 at 13:41

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See this page. The third algorithm shown is Knuth's. The algorithm is said to be "numerically stable", which implies that it avoids catastrophic cancellation, among other things.

See also here or here. The algorithm given by Knuth goes back to a 1962 paper by Welford. You will find lots of material if you google "welford mean variance".

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