In the mathematical subfield of numerical analysis the approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

1. the measurement of the data is not precise (due to the instruments), or
2. we use approximations instead of the real data (e.g., 3.14 instead of π).

One commonly distinguishes between the relative error and the absolute error.

The numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.

Definitions

Given some value a and an approximation b of a, the absolute error is

$\backslash epsilon\; =\; |a\; -\; b|\backslash ,$

the relative error is

$\backslash eta\; =\; \backslash frac\{|a\; -\; b|\}\{|a|\}$

and the percent error is

$\backslash delta\; =\; \backslash frac\{|a-b|\}\{|a|\}\backslash times\{\}100\backslash \%$

where the vertical bars denote the absolute value.

Numerical analysis

Rundungsfehler | Error de aproximación | Erreur d'approximation | Benaderingsfout | Błąd przybliżenia | Absolutfel