Catastrophic cancellation

In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one L 1 = 253.51 cm {\displaystyle L_{1}=253.51\,{\text{cm}}} long and the other L 2 = 252.49 cm {\displaystyle L_{2}=252.49\,{\text{cm}}} long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be L ~ 1 = 254 cm {\displaystyle {\tilde {L}}_{1}=254\,{\text{cm}}} and L ~ 2 = 252 cm {\displaystyle {\tilde {L}}_{2}=252\,{\text{cm}}} .

Source: Wikipedia — Catastrophic cancellation (CC BY-SA 4.0)

Catastrophic cancellation

In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one L 1 = 253.51 cm {\displaystyle L_{1}=253.51\,{\text{cm}}} long and the other L 2 = 252.49 cm {\displaystyle L_{2}=252.49\,{\text{cm}}} long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be L ~ 1 = 254 cm {\displaystyle {\tilde {L}}_{1}=254\,{\text{cm}}} and L ~ 2 = 252 cm {\displaystyle {\tilde {L}}_{2}=252\,{\text{cm}}} .

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Source: Wikipedia "Catastrophic cancellation" · CC BY-SA 4.0

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