Approximation Error - Definitions

Definitions

Given some value v and its approximation vapprox, the absolute error is

where the vertical bars denote the absolute value. If the relative error is

\eta = \frac{|v-v_\text{approx}|}{|v|} = \left| \frac{v-v_\text{approx}}{v} \right| = \left| 1 - \frac{v_\text{approx}}{v} \right|,

and the percent error is

These definitions can be extended to the case when and are n-dimensional vectors, by replacing the absolute value with an n-norm.

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