nearcancellation
Nearcancellation is a term used in numerical analysis and scientific computing to describe a situation in which the sum or difference of two large, nearly equal quantities produces a much smaller result. This effect can lead to a disproportionate loss of precision when calculations are performed with finite-precision arithmetic, such as floating-point representations. It is closely related to catastrophic cancellation, but nearcancellation emphasizes the sensitivity that arises when significant digits cancel out rather than a complete breakdown of arithmetic.
The underlying mechanism is straightforward: when two numbers have almost the same magnitude and opposite signs
Examples arise in many contexts. A classic illustration is subtracting numbers like 1e14 and 1e14+1 in double
Mitigation strategies include reformulating the computation to avoid subtracting nearly equal terms, using compensated or higher-precision