Editing Approximation error (section)

== Comparison ==
When comparing the behavior and intrinsic characteristics of these two fundamental error types, it is important to recognize their differing sensitivities to common arithmetic operations. Specifically, statements and conclusions made about ''relative errors'' are notably sensitive to the addition of a non-zero constant to the underlying true and approximated values, as such an addition alters the base value against which the error is relativized, thereby changing the ratio. However, relative errors remain unaffected by the multiplication of both the true and approximated values by the same non-zero constant, because this constant would appear in both the numerator (of the absolute error) and the denominator (the true value) of the relative error calculation, and would consequently cancel out, leaving the relative error unchanged. Conversely, for ''absolute errors'', the opposite relationship holds true: absolute errors are directly sensitive to the multiplication of the underlying values by a constant (as this scales the magnitude of the difference itself), but they are largely insensitive to the addition of a constant to these values (since adding the same constant to both the true value and its approximation does not change the difference between them: (''v''+c) − (''v''<sub>approx</sub>+c) = ''v'' − ''v''<sub>approx</sub>).<ref name=":02">{{Cite Geometric Algorithms and Combinatorial Optimization}}</ref>{{Rp|page=34}}