Approximation error

"Absolute error" redirects here. Not to be confused with Absolute deviation.
For broader coverage of this topic, see Approximation.
Graph of (blue) with its linear approximation (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.

The approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute error divided by the data value).

An approximation error can occur for a variety of reasons, among them a computing machine precision or measurement error (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.1 cm, so you measure it as 4.5 cm).

In the mathematical field of numerical analysis, the numerical stability of an algorithm indicates the extent to which errors in the input of the algorithm will lead to large errors of the output; numerically stable algorithms do not yield a significant error in output when the input is malformed and vice versa.[1]

  1. ^ Weisstein, Eric W. "Numerical Stability". mathworld.wolfram.com. Retrieved 2023-06-11.