Affine arithmetic

Summary

Affine arithmetic is a method of range analysis that represents each uncertain quantity as an affine function of shared noise symbols, each ranging over $[-1, 1]$. Because quantities that depend on the same source of error share a noise symbol, their correlations are kept. This avoids much of the overestimation of interval arithmetic, where $x - x$ for $x \in [0, 1]$ gives $[-1, 1]$ instead of $0$. Nonlinear operations are approximated by affine ones, and the approximation error becomes a new noise symbol, so the bounds remain guaranteed.