Rounding error

Error caused by representing and operating on numbers with finite precision.

Definition

Computers store real numbers in floating point with a fixed number of digits, so almost every datum and operation introduces a small error. These errors can accumulate or be amplified, especially when subtracting nearly equal numbers (cancellation).

How it is used

It is the flip side of truncation: as the step hh shrinks, truncation decreases but relative rounding grows, which imposes an optimal step in finite differences.