المدربCatastrophic cancellation is the loss of relative accuracy when two nearly equal rounded numbers are subtracted: the leading digits cancel and the rounding errors remain. Compensated summation (Kahan, 1965; in Neumaier’s variant, 1974) carries the rounding error of each addition in a separate variable and adds it back. Welford’s algorithm (1962) updates a running mean and sum of squared deviations one observation at a time.
