Approximation error

In the mathematical subfield of numerical analysis and in psychphysics 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) approximations are used instead of the real data (e.g., 3.14 instead of &pi;).

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.

Absolute error
In psychmetrics, for example, the absolute error difference between the judged value of a stimulus say approximation b and its true value a, ignoring the value of the difference. the absolute error is


 * $$\epsilon = |a - b|\,$$

Relative error
In psychometrics the relative error is the absolute error divided by the true value of the stimulus


 * $$\eta = \frac{|a - b|}{|a|} $$

Percent error
and the percent error is


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

where the vertical bars denote the absolute value, a represents the true value, and b represents the approximation to a.

Rundungsfehler Error de aproximación Erreur d'approximation Benaderingsfout Błąd przybliżenia Absolutfel 逼近误差