Catastrophic Cancellation

Shared Foundations · Numerics · catastrophic-cancellation.yaml

Subtracting two nearly equal values discards the leading digits they agree on and promotes rounding error into the result. The reason a mathematically exact rearrangement can be numerically disastrous.

Colour is the family; a dashed line is the second member of it.

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G catastrophic-cancellation Catastrophic Cancellation floating-point Floating-Point Arithmetic catastrophic-cancellation->floating-point kahan-summation Kahan Summation kahan-summation->catastrophic-cancellation recovers the low-order bits each addition throws away

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