Relative Error

Topics: Numerical Analysis

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The relative error normalises the error to the true value. It’s given by:

$$E_r=\frac{|x-x_n|}{|x|}$$

…where $x$ is the exact value we’re trying to approximate to, while $x_n$ is our last approximation.

Compare the absolute error.

If the Exact Value isn't Known

If the exact value isn’t known (i.e. we’re using a numerical method to find it), then $x$ is the last approximation we got, and $x_n$ the penultimate one.

This can only be done with convergent numerical methods, since this ensures our last approximation is better than the one before.

Relative Porcentual Error §

The relative error can also be given the in a percentage ($E_r$%):

$$\%E_r=\frac{|x-x_n|}{|x|}100\%$$