Definition:Error

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Definition

Let $x$ be an approximation to a (true) value $X$.

The error $\varepsilon$ is a measure of how much difference there is between $x$ and $X$.


Relative Error

The relative error in $x$ is defined as:

$\dfrac {\size {X - x} } X$

where $\size {X - x}$ denotes the absolute value of $X - x$.


Absolute Error

The absolute error $\varepsilon$ is the difference between $x$ and a $X$, and can be defined in one of three ways:

\(\text {(1)}: \quad\) \(\ds \varepsilon\) \(:=\) \(\ds X - x\)
\(\text {(2)}: \quad\) \(\ds \varepsilon\) \(:=\) \(\ds x - X\)
\(\text {(3)}: \quad\) \(\ds \varepsilon\) \(:=\) \(\ds \size {X - x}\)

where $\size {X - x}$ denotes the absolute value of $X - x$.

Different sources use different conventions.


Also known as

An error is also, in some branches of mathematics, known as a residual.


Also see

Not to be confused with a mistake.


Sources